chapter 5 resource masters · ©glencoe/mcgraw-hill iv glencoe algebra 1 teacher’s guide to using...
TRANSCRIPT
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
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ISBN: 0-07-827729-9 Glencoe Algebra 1Chapter 5 Resource Masters
3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04
Glencoe/McGraw-Hill
CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7Reading to Learn Mathematics Workbook 0-07-861060-5
ANSWERS FOR WORKBOOKS The answers for Chapter 5 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
StudentWorks™ This CD-ROM includes the entire Student Edition text alongwith the English workbooks listed above.
TeacherWorks™ All of the materials found in this booklet are included for view-ing and printing in the Glencoe Algebra 1 TeacherWorks CD-ROM.
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 5-1Study Guide and Intervention . . . . . . . . 281–282Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 283Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Reading to Learn Mathematics . . . . . . . . . . 285Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 286
Lesson 5-2Study Guide and Intervention . . . . . . . . 287–288Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 289Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 290Reading to Learn Mathematics . . . . . . . . . . 291Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 292
Lesson 5-3Study Guide and Intervention . . . . . . . . 293–294Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 295Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 296Reading to Learn Mathematics . . . . . . . . . . 297Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 298
Lesson 5-4Study Guide and Intervention . . . . . . . . 299–300Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 301Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 302Reading to Learn Mathematics . . . . . . . . . . 303Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 304
Lesson 5-5Study Guide and Intervention . . . . . . . . 305–306Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 307Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 308Reading to Learn Mathematics . . . . . . . . . . 309Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 310
Lesson 5-6Study Guide and Intervention . . . . . . . . 311–312Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 313Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 314Reading to Learn Mathematics . . . . . . . . . . 315Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 316
Lesson 5-7Study Guide and Intervention . . . . . . . . 317–318Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 319Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 320Reading to Learn Mathematics . . . . . . . . . . 321Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 322
Chapter 5 AssessmentChapter 5 Test, Form 1 . . . . . . . . . . . . 323–324Chapter 5 Test, Form 2A . . . . . . . . . . . 325–326Chapter 5 Test, Form 2B . . . . . . . . . . . 327–328Chapter 5 Test, Form 2C . . . . . . . . . . . 329–330Chapter 5 Test, Form 2D . . . . . . . . . . . 331–332Chapter 5 Test, Form 3 . . . . . . . . . . . . 333–334Chapter 5 Open-Ended Assessment . . . . . . 335Chapter 5 Vocabulary Test/Review . . . . . . . 336Chapter 5 Quizzes 1 & 2 . . . . . . . . . . . . . . . 337Chapter 5 Quizzes 3 & 4 . . . . . . . . . . . . . . . 338Chapter 5 Mid-Chapter Test . . . . . . . . . . . . . 339Chapter 5 Cumulative Review . . . . . . . . . . . 340Chapter 5 Standardized Test Practice . . 341–342
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 5 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 5 Resource Masters includes the core materials neededfor Chapter 5. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 5-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 5Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 314–315. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
55
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 5.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
constant of variation
direct variation
family of graphs
line of fit
linear extrapolation
ihk·STRA·puh·LAY·shun
linear interpolation
ihn·TUHR·puh·LAY·shun
negative correlation
KAWR·uh·LAY·shun
parallel lines
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
perpendicular lines
PUHR·puhn·DIH·kyuh·luhr
point-slope form
positive correlation
rate of change
scatter plot
slope
slope-intercept form
IHN·tuhr·SEHPT
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
55
Study Guide and InterventionSlope
NAME ______________________________________________ DATE ____________ PERIOD _____
5-15-1
© Glencoe/McGraw-Hill 281 Glencoe Algebra 1
Less
on
5-1
Find Slope
Slope of a Linem � or m � , where (x1, y1) and (x2, y2) are the coordinates
of any two points on a nonvertical line
y2 � y1�x2 � x1
rise�run
Find the slope of theline that passes through (�3, 5)and (4, �2).
Let (�3, 5) � (x1, y1) and (4, �2) � (x2, y2).
m � Slope formula
� y2 � �2, y1 � 5, x2 � 4, x1 � �3
� Simplify.
� �1
�7�7
�2 � 5��4 � (�3)
y2 � y1�x2 � x1
Find the value of r so that the line through (10, r) and (3, 4) has a
slope of � .
m � Slope formula
� � m � � , y2 � 4, y1 � r, x2 � 3, x1 � 10
� � Simplify.
�2(�7) � 7(4 � r) Cross multiply.
14 � 28 � 7r Distributive Property
�14 � �7r Subtract 28 from each side.
2 � r Divide each side by �7.
4 � r�
�72�7
2�7
4 � r�3 � 10
2�7
y2 � y1�x2 � x1
2�7
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find the slope of the line that passes through each pair of points.
1. (4, 9), (1, 6) 2. (�4, �1), (�2, �5) 3. (�4, �1), (�4, �5)
4. (2, 1), (8, 9) 5. (14, �8), (7, �6) 6. (4, �3), (8, �3)
7. (1, �2), (6, 2) 8. (2, 5), (6, 2) 9. (4, 3.5), (�4, 3.5)
Determine the value of r so the line that passes through each pair of points hasthe given slope.
10. (6, 8), (r, �2), m � 1 11. (�1, �3), (7, r), m � 12. (2, 8), (r, �4) m � �3
13. (7, �5), (6, r), m � 0 14. (r, 4), (7, 1), m � 15. (7, 5), (r, 9), m � 6
16. (10, r), (3, 4), m � � 17. (10, 4), (�2, r), m � �0.5 18. (r, 3), (7, r), m � �1�5
2�7
3�4
3�4
© Glencoe/McGraw-Hill 282 Glencoe Algebra 1
Rate of Change The rate of change tells, on average, how a quantity is changing overtime. Slope describes a rate of change.
POPULATION The graph shows the population growth in China.
a. Find the rates of change for 1950–1975 and for 1975–2000.
1950–1975: �
� or 0.0152
1975–2000: �
� or 0.0124
b. Explain the meaning of the slope in each case.From 1950–1975, the growth was 0.0152 billion per year, or 15.2 million per year.From 1975–2000, the growth was 0.0124 billion per year, or 12.4 million per year.
c. How are the different rates of change shown on the graph?There is a greater vertical change for 1950–1975 than for 1975–2000. Therefore, thesection of the graph for 1950–1975 has a steeper slope.
LONGEVITY The graph shows the predicted life expectancy for men and women born in a given year.
1. Find the rates of change for women from 2000–2025 and 2025–2050.
2. Find the rates of change for men from 2000–2025 and2025–2050.
3. Explain the meaning of your results in Exercises 1 and 2.
4. What pattern do you see in the increase with each 25-year period?
5. Make a prediction for the life expectancy for 2050–2075. Explain how you arrived atyour prediction.
Predicting Life Expectancy
Year Born
Ag
e
2000
WomenMen
100
95
90
85
80
75
70
65
2050*2025*
*Estimated
Source: USA TODAY
8084
8178
74
87
0.31�25
1.24 � 0.93��2000 � 1975
change in population���change in time
0.38�25
0.93 � 0.55��1975 � 1950
change in population���change in time
Population Growth in China
Year
Peo
ple
(b
illio
ns)
1950 1975 2000
2.0
1.5
1.0
0.5
02025*
*Estimated
Source: United Nations Population Division
0.550.93
1.241.48
Study Guide and Intervention (continued)
Slope
NAME ______________________________________________ DATE ____________ PERIOD _____
5-15-1
ExercisesExercises
ExampleExample
Skills PracticeSlope
NAME ______________________________________________ DATE ____________ PERIOD _____
5-15-1
© Glencoe/McGraw-Hill 283 Glencoe Algebra 1
Less
on
5-1
Find the slope of the line that passes through each pair of points.
1. 2. 3.
4. (2, 5), (3, 6) 5. (6, 1), (�6, 1)
6. (4, 6), (4, 8) 7. (5, 2), (5, �2)
8. (2, 5), (�3, �5) 9. (9, 8), (7, �8)
10. (�5, �8), (�8, 1) 11. (�3, 10), (�3, 7)
12. (17, 18), (18, 17) 13. (�6, �4), (4, 1)
14. (10, 0), (�2, 4) 15. (2, �1), (�8, �2)
16. (5, �9), (3, �2) 17. (12, 6), (3, �5)
18. (�4, 5), (�8, �5) 19. (�5, 6), (7, �8)
Find the value of r so the line that passes through each pair of points has thegiven slope.
20. (r, 3), (5, 9), m � 2 21. (5, 9), (r, �3), m � �4
22. (r, 2), (6, 3), m � 23. (r, 4), (7, 1), m �
24. (5, 3), (r, �5), m � 4 25. (7, r), (4, 6), m � 0
3�4
1�2
(0, 1)
(1, –2)x
y
O
(0, 0)
(3, 1)
x
y
O(0, 1)
(2, 5)
x
y
O
© Glencoe/McGraw-Hill 284 Glencoe Algebra 1
Find the slope of the line that passes through each pair of points.
1. 2. 3.
4. (6, 3), (7, �4) 5. (�9, �3), (�7, �5)
6. (6, �2), (5, �4) 7. (7, �4), (4, 8)
8. (�7, 8), (�7, 5) 9. (5, 9), (3, 9)
10. (15, 2), (�6, 5) 11. (3, 9), (�2, 8)
12. (�2, �5), (7, 8) 13. (12, 10), (12, 5)
14. (0.2, �0.9), (0.5, �0.9) 15. � , �, �� , �
Find the value of r so the line that passes through each pair of points has thegiven slope.
16. (�2, r), (6, 7), m � 17. (�4, 3), (r, 5), m �
18. (�3, �4), (�5, r), m � � 19. (�5, r), (1, 3), m �
20. (1, 4), (r, 5), m undefined 21. (�7, 2), (�8, r), m � �5
22. (r, 7), (11, 8), m � � 23. (r, 2), (5, r), m � 0
24. ROOFING The pitch of a roof is the number of feet the roof rises for each 12 feethorizontally. If a roof has a pitch of 8, what is its slope expressed as a positive number?
25. SALES A daily newspaper had 12,125 subscribers when it began publication. Five yearslater it had 10,100 subscribers. What is the average yearly rate of change in the numberof subscribers for the five-year period?
1�5
7�6
9�2
1�4
1�2
2�3
1�3
4�3
7�3
(–2, 3)(3, 3)
x
y
O
(3, 1)
(–2, –3)
x
y
O(–1, 0)
(–2, 3)
x
y
O
Practice Slope
NAME ______________________________________________ DATE ____________ PERIOD _____
5-15-1
Reading to Learn MathematicsSlope
NAME ______________________________________________ DATE______________ PERIOD _____
5-15-1
© Glencoe/McGraw-Hill 285 Glencoe Algebra 1
Less
on
5-1
Pre-Activity Why is slope important in architecture?
Read the introduction to Lesson 5-1 at the top of page 256 in your textbook. Then complete the definition of slope and fill in the boxeson the graph with the words rise and run.
slope �
In this graph, the rise is units, and the run is units.
Thus, the slope of this line is or .
Reading the Lesson1. Describe each type of slope and include a sketch.
Type of Slope Description of Graph Sketch
positive The graph rises as you go from left to right.
negative The graph falls as you go from left to right.
zero The graph is a horizontal line.
undefined The graph is a vertical line.
2. Describe how each expression is related to slope.
a. difference of y-coordinates divided by difference ofcorresponding x-coordinates
b. how far up or down as compared to how far left or right
c. slope used as rate of change
Helping You Remember3. The word rise is usually associated with going up. Sometimes going from one point on
the graph does not involve a rise and a run but a fall and a run. Describe how you couldselect points so that it is always a rise from the first point to the second point.Sample answer: If the slope is negative, choose the second point so that its x-coordinate is less than that of the first point.
$52,000 increase in spending����26 months
rise�run
y2 � y1�x2 � x1
3�5
3 units�5 units
53
rise�run
x
y
O
© Glencoe/McGraw-Hill 286 Glencoe Algebra 1
Treasure Hunt with SlopesUsing the definition of slope, draw lines with the slopes listed below. A correct solution will trace the route to the treasure.
1. 3 2. 3. � 4. 0
5. 1 6. �1 7. no slope 8.
9. 10. 11. � 12. 33�4
1�3
3�2
2�7
2�5
1�4
Start Here
Treasure
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-15-1
Study Guide and InterventionSlope and Direct Variation
NAME ______________________________________________ DATE ____________ PERIOD _____
5-25-2
© Glencoe/McGraw-Hill 287 Glencoe Algebra 1
Less
on
5-2
Direct Variation A direct variation is described by an equation of the form y � kx,where k � 0. We say that y varies directly as x. In the equation y � kx, k is the constant of variation.
Name the constant ofvariation for the equation. Then findthe slope of the line that passesthrough the pair of points.
For y � x, the constant of variation is .
m � Slope formula
� (x1, y1) � (0, 0), (x2, y2) � (2, 1)
� Simplify.
The slope is .1�2
1�2
1 � 0�2 � 0
y2 � y1�x2 � x1
1�2
1�2
(2, 1)(0, 0) x
y
Oy � 12x
Suppose y variesdirectly as x, and y � 30 when x � 5.
a. Write a direct variation equationthat relates x and y.Find the value of k.
y � kx Direct variation equation
30 � k(5) Replace y with 30 and x with 5.
6 � k Divide each side by 5.
Therefore, the equation is y � 6x.
b. Use the direct variation equation tofind x when y � 18.
y � 6x Direct variation equation
18 � 6x Replace y with 18.
3 � x Divide each side by 6.
Therefore, x � 3 when y � 18.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.
1. 2. 3.
Write a direct variation equation that relates x to y. Assume that y varies directlyas x. Then solve.
4. If y � 4 when x � 2, find y when x � 16.
5. If y � 9 when x � �3, find x when y � 6.
6. If y � �4.8 when x � �1.6, find x when y � �24.
7. If y � when x � , find x when y � .3
�161�8
1�4
(–2, –3)
(0, 0)x
y
O
y � 32x
(1, 3)
(0, 0) x
y
O
y � 3x(–1, 2)
(0, 0)x
y
Oy � –2x
© Glencoe/McGraw-Hill 288 Glencoe Algebra 1
Solve Problems The distance formula d � rt is a direct variation equation. In theformula, distance d varies directly as time t, and the rate r is the constant of variation.
TRAVEL A family drove their car 225 miles in 5 hours.
a. Write a direct variation equation to find the distance traveled for any numberof hours.Use given values for d and t to find r.
d � rt Original equation
225 � r(5) d � 225 and t � 5
45 � r Divide each side by 5.
Therefore, the direct variation equation is d � 45t.b. Graph the equation.
The graph of d � 45t passes through the origin withslope 45.
m �
✓CHECK (5, 225) lies on the graph.c. Estimate how many hours it would take the
family to drive 360 miles.d � 45t Original equation
360 � 45t Replace d with 360.
t � 8 Divide each side by 45.
Therefore, it will take 8 hours to drive 360 miles.
RETAIL The total cost C of bulk jelly beans is $4.49 times the number of pounds p.
1. Write a direct variation equation that relates the variables.
2. Graph the equation on the grid at the right.
3. Find the cost of pound of jelly beans.
CHEMISTRY Charles’s Law states that, at a constant pressure, volume of a gas V varies directly as its temperatureT. A volume of 4 cubic feet of a certain gas has a temperatureof 200° (absolute temperature).
4. Write a direct variation equation that relates the variables.
5. Graph the equation on the grid at the right.
6. Find the volume of the same gas at 250° (absolute temperature).
Charles’s Law
Temperature (�K)
Vo
lum
e (c
ub
ic f
eet)
1000 200 T
V
4
3
2
1
3�4
Cost of Jelly Beans
Weight (pounds)
Co
st (
do
llars
)
20 4 w
C
18.00
13.50
9.00
4.50
rise�run
45�1
Automobile Trips
Time (hours)
Dis
tan
ce (
mile
s)10 2 3 4 5 6 7 8 t
d
360
270
180
90(1, 45)
(5, 225)d � 45t
Study Guide and Intervention (continued)
Slope and Direct Variation
NAME ______________________________________________ DATE ____________ PERIOD _____
5-25-2
ExampleExample
ExercisesExercises
Skills PracticeSlope and Direct Variation
NAME ______________________________________________ DATE ____________ PERIOD _____
5-25-2
© Glencoe/McGraw-Hill 289 Glencoe Algebra 1
Less
on
5-2
Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.
1. 2. 3.
Graph each equation.
4. y � 3x 5. y � � x 6. y � x
Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.
7. If y � �8 when x � �2, find x 8. If y � 45 when x � 15, find xwhen y � 32. when y � 15.
9. If y � �4 when x � 2, find y 10. If y � �9 when x � 3, find ywhen x � �6. when x � �5.
11. If y � 4 when x � 16, find y 12. If y � 12 when x � 18, find xwhen x � 6. when y � �16.
Write a direct variation equation that relates the variables. Then graph theequation.
13. TRAVEL The total cost C of gasoline 14. SHIPPING The number of delivered toys Tis $1.80 times the number of gallons g. is 3 times the total number of crates c.
Toys Shipped
Crates
Toys
20 4 6 71 3 5 c
T
21
18
15
12
9
6
3
Gasoline Cost
Gallons
Co
st (
$)
40 8 12 142 6 10 g
C
28
24
20
16
12
8
4
x
y
O
2�5
x
y
O
3�4
x
y
O
(–2, 3)
(0, 0)x
y
O
y � – 32x
(–1, 2)(0, 0)
x
y
O
y � –2x
(3, 1)(0, 0)
x
y
O
y � 13x
© Glencoe/McGraw-Hill 290 Glencoe Algebra 1
Name the constant of variation for each equation. Then determine the slope of theline that passes through each pair of points.
1. ; 2. ; 3. � ;�
Graph each equation.
4. y � �2x 5. y � x 6. y � � x
Write a direct variation equation that relates x and y. Assume that y variesdirectly as x. Then solve.
7. If y � 7.5 when x � 0.5, find y when x � �0.3. y � 15x; �4.5
8. If y � 80 when x � 32, find x when y � 100. y � 2.5x; 40
9. If y � when x � 24, find y when x � 12. y � x;
Write a direct variation equation that relates the variables. Then graph theequation.
10. MEASURE The width W of a 11. TICKETS The total cost C of tickets isrectangle is two thirds of the length �. $4.50 times the number of tickets t.
W � � C � 4.50t
12. PRODUCE The cost of bananas varies directly with their weight. Miguel bought
3 pounds of bananas for $1.12. Write an equation that relates the cost of the bananas
to their weight. Then find the cost of 4 pounds of bananas. C � 0.32p; $1.361�4
1�2
Rectangle Dimensions
Length
Wid
th
40 8 122 6 10 �
W
10
8
6
4
2
2�3
3�8
1�32
3�4
5�3
x
y
O
6�5
x
y
O
5�2
5�2
(–2, 5)
(0, 0)x
y
O
y � � 52x
4�3
4�3(3, 4)
(0, 0)x
y
O
y � 43x
3�4
3�4
(4, 3)
(0, 0)x
y
O
y � 34x
Practice (Average)
Slope and Direct Variation
NAME ______________________________________________ DATE______________ PERIOD _____
5-25-2
Reading to Learn MathematicsSlope and Direct Variation
NAME ______________________________________________ DATE______________ PERIOD _____
5-25-2
© Glencoe/McGraw-Hill 291 Glencoe Algebra 1
Less
on
5-2
Pre-Activity How is slope related to your shower?
Read the introduction to Lesson 5-2 at the top of page 264 in your textbook.
• How do the numbers in the table relate to the graph shown?They are the coordinates of the points on the graph.
• Think about the first sentence. What does it mean to say that a standardshowerhead uses about 6 gallons of water per minute?Sample answer: For each minute the shower runs, 6 gallonsof water come out. So, if the shower ran 10 minutes, thatwould be 60 gallons.
Reading the Lesson
1. What is the form of a direct variation equation? y � kx
2. How is the constant of variation related to slope? The constant of variation hasthe same value as the slope of the graph of the equation.
3. The expression “y varies directly as x” can be written as the equation y � kx. How wouldyou write an equation for “w varies directly as the square of t”? w � kt2
4. For each situation, write an equation with the proper constant of variation.
a. The distance d varies directly as time t, and a cheetah can travel 88 feet in 1 second.d � 88t
b. The perimeter p of a pentagon with all sides of equal length varies directly as thelength s of a side of the pentagon. A pentagon has 5 sides. p � 5s
c. The wages W earned by an employee vary directly with the number of hours h thatare worked. Enrique earned $172.50 for 23 hours of work. W � $7.50h
Helping You Remember
5. Look up the word constant in a dictionary. How does this definition relate to the termconstant of variation? Sample answer: Something unchanging; the constantof variation relates x and y in the same value every time, and thatrelationship never changes.
© Glencoe/McGraw-Hill 292 Glencoe Algebra 1
nth Power VariationAn equation of the form y � kxn, where k � 0, describes an nth powervariation. The variable n can be replaced by 2 to indicate the second powerof x (the square of x) or by 3 to indicate the third power of x (the cube of x).
Assume that the weight of a person of average build varies directly as thecube of that person’s height. The equation of variation has the form w � kh3.
The weight that a person’s legs will support is proportional to the cross-sectional area of the leg bones. This area varies directly as the squareof the person’s height. The equation of variation has the form s � kh2.
Answer each question.
1. For a person 6 feet tall who weighs 200 pounds, find a value for k in the equation w � kh3.
2. Use your answer from Exercise 1 to predict the weight of a person who is 5 feet tall.
3. Find the value for k in the equation w � kh3 for a baby who is 20 inches long and weighs 6 pounds.
4. How does your answer to Exercise 3 demonstrate that a baby is significantly fatter in proportion to its height than an adult?
5. For a person 6 feet tall who weighs 200 pounds, find a value for k in the equation s � kh2.
6. For a baby who is 20 inches long and weighs 6 pounds, find an “infant value” for k in the equation s � kh2.
7. According to the adult equation you found (Exercise 1), how much would an imaginary giant 20 feet tall weigh?
8. According to the adult equation for weight supported (Exercise 5), how much weight could a 20-foot tall giant’s legs actually support?
9. What can you conclude from Exercises 7 and 8?
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-25-2
Study Guide and InterventionSlope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-35-3
© Glencoe/McGraw-Hill 293 Glencoe Algebra 1
Less
on
5-3
Slope-Intercept Form
Slope-Intercept Form y � mx � b, where m is the given slope and b is the y-intercept
Write an equation of the line whose slope is �4 and whose y-intercept is 3.y � mx � b Slope-intercept form
y � �4x � 3 Replace m with �4 and b with 3.
Graph 3x � 4y � 8.
3x � 4y � 8 Original equation
�4y � �3x � 8 Subtract 3x from each side.
� Divide each side by �4.
y � x � 2 Simplify.
The y-intercept of y � x � 2 is �2 and the slope is . So graph the point (0, �2). From
this point, move up 3 units and right 4 units. Draw a line passing through both points.
Write an equation of the line with the given slope and y-intercept.
1. slope: 8, y-intercept �3 2. slope: �2, y-intercept �1 3. slope: �1, y-intercept �7
Write an equation of the line shown in each graph.
4. 5. 6.
Graph each equation.
7. y � 2x � 1 8. y � �3x � 2 9. y � �x � 1
x
y
Ox
y
Ox
y
O
(4, –2)
(0, –5)
xy
O
(3, 0)
(0, 3)
x
y
O(0, –2)
(1, 0) x
y
O
3�4
3�4
3�4
�3x � 8��
�4�4y��4
(0, –2)
(4, 1)
x
y
O
3x � 4y � 8
Example 1Example 1
Example 2Example 2
ExercisesExercises
© Glencoe/McGraw-Hill 294 Glencoe Algebra 1
Model Real-World Data
MEDIA Since 1997, the number of cable TV systems has decreasedby an average rate of 121 systems per year. There were 10,943 systems in 1997.
a. Write a linear equation to find the average number of cable systems in any yearafter 1997.The rate of change is �121 systems per year. In the first year, the number of systems was10,943. Let N � the number of cable TV systems. Let x � the number of years after 1997.An equation is N � �121x � 10,943.
b. Graph the equation.The graph of N � �121x � 10,943 is a line that passesthrough the point at (0, 10,943) and has a slope of �121.
c. Find the approximate number of cable TV systems in 2000.N � �121x � 10,943 Original equation
N � �121(3) � 10,943 Replace x with 3.
N � 10,580 Simplify.
There were about 10,580 cable TV systems in 2000.
ENTERTAINMENT In 1995, 65.7% of all households with TV’s in the U.S. subscribed to cable TV. Between 1995and 1999, the percent increased by about 0.6% each year.
1. Write an equation to find the percent P of households thatsubscribed to cable TV for any year x between 1995 and 1999.
2. Graph the equation on the grid at the right.
3. Find the percent that subscribed to cable TV in 1999.
POPULATION The population of the United States is projected to be 300 million by the year 2010. Between 2010 and 2050, the population is expected to increase byabout 2.5 million per year.
4. Write an equation to find the population P in any year xbetween 2010 and 2050.
5. Graph the equation on the grid at the right.
6. Find the population in 2050.
Projected UnitedStates Population
Years Since 2010
Pop
ula
tio
n (
mill
ion
s)
0 20 40 x
P
400
380
360
340
320
300
Source: The World Almanac
Percent of Householdswith TV Having Cable
Years Since 1995
Perc
ent
10 2 3 4 5 x
P
68
67
66
65
Source: The World Almanac
Cable TV Systems
Years Since 1997
Nu
mb
er o
f C
able
TV
Sys
tem
s
10 2 3 4 5 6 x
N
10,900
10,800
10,700
10,600
10,500
Source: The World Almanac
Study Guide and Intervention (continued)
Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-35-3
ExampleExample
ExercisesExercises
Skills PracticeSlope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-35-3
© Glencoe/McGraw-Hill 295 Glencoe Algebra 1
Less
on
5-3
Write an equation of the line with the given slope and y-intercept.
1. slope: 5, y-intercept: �3 2. slope: �2, y-intercept: 7
3. slope: �6, y-intercept: �2 4. slope: 7, y-intercept: 1
5. slope: 3, y-intercept: 2 6. slope: �4, y-intercept: �9
7. slope: 1, y-intercept: �12 8. slope: 0, y-intercept: 8
Write an equation of the line shown in each graph.
9. 10. 11.
Graph each equation.
12. y � x � 4 13. y � �2x � 1 14. x � y � �3
Write a linear equation in slope-intercept form to model each situation.
15. A video store charges $10 for a rental card plus $2 per rental.
16. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year.
17. A Cairn terrier weighs 30 pounds and is on a special diet to lose 2 pounds per month.
18. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.
x
y
O
x
y
Ox
y
O
(0, –1)(2, –3)
x
y
O
(0, 2)
(2, –4)
x
y
O(2, 1)
(0, –3)
x
y
O
© Glencoe/McGraw-Hill 296 Glencoe Algebra 1
Write an equation of the line with the given slope and y-intercept.
1. slope: , y-intercept: 3 2. slope: , y-intercept: �4
3. slope: 1.5, y-intercept: �1 4. slope: �2.5, y-intercept: 3.5
Write an equation of the line shown in each graph.
5. 6. 7.
Graph each equation.
8. y � � x � 2 9. 3y � 2x � 6 10. 6x � 3y � 6
Write a linear equation in slope-intercept form to model each situation.
11. A computer technician charges $75 for a consultation plus $35 per hour.
12. The population of Pine Bluff is 6791 and is decreasing at the rate of 7 per year.
WRITING For Exercises 13–15, use the following information.Carla has already written 10 pages of a novel. She plansto write 15 additional pages per month until she is finished.
13. Write an equation to find the total number of pages Pwritten after any number of months m.
14. Graph the equation on the grid at the right.
15. Find the total number of pages written after 5 months.
Carla’s Novel
Months
Pag
es W
ritt
en
20 4 61 3 5 m
P
100
80
60
40
20
x
y
Ox
y
O
1�2
(–3, 0)
(0, –2)
x
y
O(–2, 0)
(0, 3)
x
y
O(–5, 0)
(0, 2)
x
y
O
3�2
1�4
Practice Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-35-3
Reading to Learn MathematicsSlope-Intercept Form
NAME ______________________________________________ DATE______________ PERIOD _____
5-35-3
© Glencoe/McGraw-Hill 297 Glencoe Algebra 1
Less
on
5-3
Pre-Activity How is a y-intercept related to a flat fee?
Read the introduction to Lesson 5-3 at the top of page 272 in your textbook.
• What point on the graph shows that the flat fee is $5.00?
• How does the rate of $0.10 per minute relate to the graph?
Reading the Lesson
1. Fill in the boxes with the correct words to describe what m and b represent.
y � mx � b↑ ↑
2. What are the slope and y-intercept of a vertical line?
The slope is undefined, and there is no y-intercept.
3. What are the slope and y-intercept of a horizontal line?
The slope is 0, and the y-intercept is where it crosses the y-axis.
4. Read the problem. Then answer each part of the exercise.
A ruby-throated hummingbird weighs about 0.6 gram at birth and gains weight at a rateof about 0.2 gram per day until fully grown.
a. Write a verbal equation to show how the words are related to finding the averageweight of a ruby-throated hummingbird at any given week. Use the words weight atbirth, rate of growth, weight, and weeks after birth. Below the equation, fill in anyvalues you know and put a question mark under the items that you do not know.
� � �
b. Define what variables to use for the unknown quantities.
c. Use the variables you defined and what you know from the problem to write anequation.
Helping You Remember
5. One way to remember something is to explain it to another person. Write how you wouldexplain to someone the process for using the y-intercept and slope to graph a linearequation.
weight?
rate of growth0.2
weeks after birth?
weight at birth0.6
© Glencoe/McGraw-Hill 298 Glencoe Algebra 1
Relating Slope-Intercept Form and Standard Forms
You have learned that slope can be defined in terms of or .
Another definition can be found from the standard from of a linear equation. Standard form is Ax � By � C, where A, B, and C are integers, A � 0, and A and B are not both zero.
1. Solve Ax � By � C for y. Your answer should be written in slope-intercept form.
2. Use the slope-intercept equation you wrote in Exercise 1 to write expressions for the slope and the y-intercept in terms of A, B, and C.
Use the expressions in Exercise 2 above to find the slope and y-intercept of each equation.
3. 2x � y � �4 4. 4x � 3y � 24
5. 4x � 6y � �36 6. x � 3y � �27
7. x � 2y � 6 8. 4y � 20
y2 � y1�x2 � x1
rise�run
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-35-3
Study Guide and InterventionWriting Equations in Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-45-4
© Glencoe/McGraw-Hill 299 Glencoe Algebra 1
Less
on
5-4
Write an Equation Given the Slope and One Point
Write an equation ofa line that passes through (�4, 2)with slope 3.
The line has slope 3. To find the y-intercept, replace m with 3 and (x, y)with (�4, 2) in the slope-intercept form.Then solve for b.
y � mx � b Slope-intercept form
2 � 3(�4) � b m � 3, y � 2, and x � �4
2 � �12 � b Multiply.
14 � b Add 12 to each side.
Therefore, the equation is y � 3x � 14.
Write an equation of the linethat passes through (�2, �1) with slope .
The line has slope . Replace m with and (x, y)
with (�2, �1) in the slope-intercept form.
y � mx � b Slope-intercept form
�1 � (�2) � b m � , y � �1, and x � �2
�1 � � � b Multiply.
� � b Add to each side.
Therefore, the equation is y � x � .1�2
1�4
1�2
1�2
1�2
1�4
1�4
1�4
1�4
1�4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Write an equation of the line that passes through each point with the given slope.
1. 2. 3.
4. (8, 2), m � � 5. (�1, �3), m � 5 6. (4, �5), m � �
7. (�5, 4), m � 0 8. (2, 2), m � 9. (1, �4), m � �6
10. Write an equation of a line that passes through the y-intercept �3 with slope 2.
11. Write an equation of a line that passes through the x-intercept 4 with slope �3.
12. Write an equation of a line that passes through the point (0, 350) with slope .1�5
1�2
1�2
3�4
(2, 4)
x
y
O
m � 12
(0, 0)x
y
O
m � –2
(3, 5)
x
y
O
m � 2
© Glencoe/McGraw-Hill 300 Glencoe Algebra 1
Write an Equation Given Two Points
Write an equation of the line that passes through (1, 2) and (3, �2).
Find the slope m. To find the y-intercept, replace m with its computed value and (x, y) with(1, 2) in the slope-intercept form. Then solve for b.
m � Slope formula
m � y2 � �2, y1 � 2, x2 � 3, x1 � 1
m � �2 Simplify.
y � mx � b Slope-intercept form
2 � �2(1) � b Replace m with �2, y with 2, and x with 1.
2 � �2 � b Multiply.
4 � b Add 2 to each side.
Therefore, the equation is y � �2x � 4.
Write an equation of the line that passes through each pair of points.
1. 2. 3.
4. (�1, 6), (7, �10) 5. (0, 2), (1, 7) 6. (6, �25), (�1, 3)
7. (�2, �1), (2, 11) 8. (10, �1), (4, 2) 9. (�14, �2), (7, 7)
10. Write an equation of a line that passes through the x-intercept 4 and y-intercept �2.
11. Write an equation of a line that passes through the x-intercept �3 and y-intercept 5.
12. Write an equation of a line that passes through (0, 16) and (�10, 0).
(0, 1)
(–3, 0) x
y
O
(0, 4)
(4, 0) x
y
O
(1, 1)
(0, –3)
x
y
O
�2 � 2�3 �1
y2 � y1�x2 � x1
Study Guide and Intervention (continued)
Writing Equations in Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-45-4
ExampleExample
ExercisesExercises
Skills PracticeWriting Equations in Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-45-4
© Glencoe/McGraw-Hill 301 Glencoe Algebra 1
Less
on
5-4
Write an equation of the line that passes through each point with the given slope.
1. 2. 3.
4. (1, 9), m � 4 5. (4, 2), m � �2 6. (2, �2), m � 3
7. (3, 0), m � 5 8. (�3, �2), m � 2 9. (�5, 4), m � �4
Write an equation of the line that passes through each pair of points.
10. 11. 12.
13. (1, 3), (�3, �5) 14. (1, 4), (6, �1) 15. (1, �1), (3, 5)
16. (�2, 4), (0, 6) 17. (3, 3), (1, �3) 18. (�1, 6), (3, �2)
Write an equation of the line that has each pair of intercepts.
19. x-intercept: �3, y-intercept: 6 20. x-intercept: 3, y-intercept: 3
21. x-intercept: 1, y-intercept: 2 22. x-intercept: 2, y-intercept: �4
23. x-intercept: �4, y-intercept: �8 24. x-intercept: �1, y-intercept: 4
(2, –1)
(0, 3)
x
y
O(–1, –3)
(1, 1)x
y
O
(–2, 3)
(3, –2)
x
y
O
(–1, 2)
x
y
O
m � 2
(4, 1)
x
y
O
m � 1
(–1, 4)
x
y
O
m � –3
© Glencoe/McGraw-Hill 302 Glencoe Algebra 1
Write an equation of the line that passes through each point with the given slope.
1. 2. 3.
4. (�5, 4), m � �3 5. (4, 3), m � 6. (1, �5), m � �
Write an equation of the line that passes through each pair of points.
7. 8. 9.
10. (0, �4), (5, �4) 11. (�4, �2), (4, 0) 12. (�2, �3), (4, 5)
13. (0, 1), (5, 3) 14. (�3, 0), (1, �6) 15. (1, 0), (5, �1)
Write an equation of the line that has each pair of intercepts.
16. x-intercept: 2, y-intercept: �5 17. x-intercept: 2, y-intercept: 10
18. x-intercept: �2, y-intercept: 1 19. x-intercept: �4, y-intercept: �3
20. DANCE LESSONS The cost for 7 dance lessons is $82. The cost for 11 lessons is $122.Write a linear equation to find the total cost C for � lessons. Then use the equation tofind the cost of 4 lessons.
21. WEATHER It is 76°F at the 6000-foot level of a mountain, and 49°F at the 12,000-footlevel of the mountain. Write a linear equation to find the temperature T at an elevatione on the mountain, where e is in thousands of feet.
(–3, 1)
(–1, –3)
x
y
O(0, 5)
(4, 1)x
y
O
(4, –2)
(2, –4)
xy
O
3�2
1�2
(–1, –3)
x
y
O
m � –1
(–2, 2)
x
y
O
m � –2
(1, 2)
x
y
Om � 3
Practice Writing Equations in Slope-Intercept Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-45-4
Reading to Learn MathematicsWriting Equations in Slope-Intercept Form
NAME ______________________________________________ DATE______________ PERIOD _____
5-45-4
© Glencoe/McGraw-Hill 303 Glencoe Algebra 1
Less
on
5-4
Pre-Activity How can slope-intercept form be used to make predictions?
Read the introduction to Lesson 5-4 at the top of page 280 in your textbook.
• What is the rate of change per year? about 2000 per year• Study the pattern on the graph. How would you find the population in
1997? Add 2000 to the 1996 population, which gives 179,000.
Reading the Lesson
1. Suppose you are given that a line goes through (2, 5) and has a slope of �2. Use thisinformation to complete the following equation.
y � mx � b↓ ↓� � �
2. What must you first do if you are not given the slope in the problem?
Use the information given (two points) to find the slope.
3. What is the first step in answering any standardized test practice question?
Read the problem.
4. What are four steps you can use in solving a word problem?
Explore, Plan, Solve, Examine
5. Define the term linear extrapolation.
Linear extrapolation means using a linear equation to predict values thatare outside the two given data points.
Helping You Remember
6. In your own words, explain how you would answer a question that asks you to write the slope-intercept form of an equation. Sample answer: Determine whatinformation you are given. If you have a point and the slope, you cansubstitute the x- and y-values and the slope into y � mx � b to find thevalue of b. Then use the values of m and b to write the equation. If youhave two points, use them to find the slope, and then use the method fora point and the slope.
b2�25
© Glencoe/McGraw-Hill 304 Glencoe Algebra 1
Celsius and Kelvin TemperaturesIf you blow up a balloon and put it in the refrigerator, the balloon will shrink as the temperature of the air in the balloon decreases.
The volume of a certain gas is measured at 30° Celsius. The temperature is decreased and the volume is measured again.
1. Graph this table on the coordinate plane provided below.
2. Find the equation of the line that passes through the points you graphed in Exercise 1.
v � t � 182
3. Use the equation you found in Exercise 2 to find the temperature that would give a volume of zero. This temperature is the lowest one possible and is called absolute zero.
�273�C
4. In 1848, Lord Kelvin proposed a new temperature scale with 0 being assigned to absolute zero. The size of the degree chosen was the same size as the Celsius degree. Change each of the Celsius temperatures in the table above to degrees Kelvin.
303�, 294�, 273�, 261�, 246�
2�3
t (�C)
V(mL)
O
200
100
10�10�20�30 20 30
Temperature (t ) Volume (V )
30°C 202 mL21°C 196 mL0°C 182 mL
–12°C 174 mL–27°C 164 mL
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
5-45-4
Study Guide and InterventionWriting Equations in Point-Slope Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-55-5
© Glencoe/McGraw-Hill 305 Glencoe Algebra 1
Less
on
5-5
Point-Slope Form
Point-Slope Formy � y1 � m(x � x1), where (x1, y1) is a given point on a nonvertical line and m is the slope of the line
Write the point-slope formof an equation for a line that passes through (6, 1) and has a slope of � .
y � y1 � m(x � x1) Point-slope form
y � 1 � � (x � 6) m � � ; (x1, y1) � (6, 1)
Therefore, the equation is y � 1� � (x � 6).5�2
5�2
5�2
5�2
Write the point-slopeform of an equation for a horizontalline that passes through (4, �1).
y � y1 � m(x � x1) Point-slope form
y � (�1) � 0(x � 4) m � 0; (x1, y1) � (4, �1)
y � 1 � 0 Simplify.
Therefore, the equation is y � 1 � 0.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Write the point-slope form of an equation for a line that passes through eachpoint with the given slope.
1. 2. 3.
4. (2, 1), m � 4 5. (�7, 2), m � 6 6. (8, 3), m � 1
7. (�6, 7), m � 0 8. (4, 9), m � 9. (�4, �5), m � �
10. Write the point-slope form of an equation for the horizontal line that passes through (4, �2).
11. Write the point-slope form of an equation for the horizontal line that passes through (�5, 6).
12. Write the point-slope form of an equation for the horizontal line that passes through (5, 0).
1�2
3�4
(2, –3)
x
y
O
m � –2
(–3, 2)
x
y
O
m � 0(4, 1)
x
y
O
m � 1
© Glencoe/McGraw-Hill 306 Glencoe Algebra 1
Forms of Linear Equations
Slope-Intercept Form
y � mx � b m � slope; b � y-intercept
Point-Slope Form
y � y1 � m(x � x1) m � slope; (x1, y1) is a given point.
Standard Ax � By � C A and B are not both zero. Usually A is nonnegative and A, B, and CForm are integers whose greatest common factor is 1.
Study Guide and Intervention (continued)
Writing Equations in Point-Slope Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-55-5
Write y � 5 � (x � 6) instandard form.
y � 5 � (x � 6) Original equation
3( y � 5) � 3� �(x � 6) Multiply each side by 3.
3y � 15 � 2(x � 6) Distributive Property
3y � 15 � 2x � 12 Distributive Property
3y � 2x � 27 Subtract 15 from each side.
�2x � 3y � �27 Add �2x to each side.
2x � 3y � 27 Multiply each side by �1.
Therefore, the standard form of the equationis 2x � 3y � 27.
2�3
2�3
2�3
Write y � 2 � � (x � 8)in slope-intercept form.
y � 2 � � (x � 8) Original equation
y � 2 � � x � 2 Distributive Property
y � � x � 4 Add 2 to each side.
Therefore, the slope-intercept form of the
equation is y � � x � 4.1�4
1�4
1�4
1�4
1�4
Example 1Example 1 Example 2Example 2
Write each equation in standard form.
1. y � 2 � �3(x � 1) 2. y � 1 � � (x � 6) 3. y � 2 � (x � 9)
4. y � 3 � �(x � 5) 5. y � 4 � (x � 3) 6. y � 4 � � (x � 1)
Write each equation in slope-intercept form.
7. y � 4 � 4(x � 2) 8. y � 5 � (x � 6) 9. y � 8 � � (x � 8)
10. y � 6 � 3�x � � 11. y � 4 � �2(x � 5) 12. y � � (x � 2)1�2
5�3
1�3
1�4
1�3
2�5
5�3
2�3
1�3
ExercisesExercises
Skills PracticeWriting Equations in Point-Slope Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-55-5
© Glencoe/McGraw-Hill 307 Glencoe Algebra 1
Less
on
5-5
Write the point-slope form of an equation for a line that passes through eachpoint with the given slope.
1. 2. 3.
4. (3, 1), m � 0 5. (�4, 6), m � 8 6. (1, �3), m � �4
7. (4, �6), m � 1 8. (3, 3), m � 9. (�5, �1), m � �
Write each equation in standard form.
10. y � 1 � x � 2 11. y � 9 � �3(x � 2) 12. y � 7 � 4(x � 4)
13. y � 4 � �(x � 1) 14. y � 6 � 4(x � 3) 15. y � 5 � �5(x � 3)
16. y � 10 � �2(x � 3) 17. y � 2 � � (x � 4) 18. y � 11 � (x � 3)
Write each equation in slope-intercept form.
19. y � 4 � 3(x � 2) 20. y � 2 � �(x � 4) 21. y � 6 � �2(x � 2)
22. y � 1 � �5(x � 3) 23. y � 3 � 6(x � 1) 24. y � 8 � 3(x � 5)
25. y � 2 � (x � 6) 26. y � 1 � � (x � 9) 27. y � � x �1�2
1�2
1�3
1�2
1�3
1�2
5�4
4�3
(2, –3)
x
y
O
m � 0
(1, –2)x
y
O
m � –1
(–1, –2)x
y
O
m � 3
© Glencoe/McGraw-Hill 308 Glencoe Algebra 1
Write the point-slope form of an equation for a line that passes through eachpoint with the given slope.
1. (2, 2), m � �3 2. (1, �6), m � �1 3. (�3, �4), m � 0
4. (1, 3), m � � 5. (�8, 5), m � � 6. (3, �3), m �
Write each equation in standard form.
7. y � 11 � 3(x � 2) 8. y � 10 � �(x � 2) 9. y � 7 � 2(x � 5)
10. y � 5 � (x � 4) 11. y � 2 � � (x � 1) 12. y � 6 � (x � 3)
13. y � 4 � 1.5(x � 2) 14. y � 3 � �2.4(x � 5) 15. y � 4 � 2.5(x � 3)
Write each equation in slope-intercept form.
16. y � 2 � 4(x � 2) 17. y � 1 � �7(x � 1) 18. y � 3 � �5(x � 12)
19. y � 5 � (x � 4) 20. y � � �3�x � � 21. y � � �2�x � �
CONSTRUCTION For Exercises 22–24, use the following information.A construction company charges $15 per hour for debris removal, plus a one-time fee for theuse of a trash dumpster. The total fee for 9 hours of service is $195.
22. Write the point-slope form of an equation to find the total fee y for any number of hours x.
23. Write the equation in slope-intercept form.
24. What is the fee for the use of a trash dumpster?
MOVING For Exercises 25–27, use the following information.There is a set daily fee for renting a moving truck, plus a charge of $0.50 per mile driven.It costs $64 to rent the truck on a day when it is driven 48 miles.
25. Write the point-slope form of an equation to find the total charge y for any number ofmiles x for a one-day rental.
26. Write the equation in slope-intercept form.
27. What is the daily fee?
1�4
2�3
1�4
1�4
3�2
4�3
3�4
3�2
1�3
2�5
3�4
Practice Writing Equations in Point-Slope Form
NAME ______________________________________________ DATE ____________ PERIOD _____
5-55-5
Reading to Learn MathematicsWriting Equations in Point-Slope Form
NAME ______________________________________________ DATE______________ PERIOD _____
5-55-5
© Glencoe/McGraw-Hill 309 Glencoe Algebra 1
Less
on
5-5
Pre-Activity How can you use the slope formula to write an equation of a line?
Read the introduction to Lesson 5-5 at the top of page 286 in your textbook.
Note that in the final equation there is a value subtracted from x and from y. What are these values?The value subtracted from x is the x-coordinate of the givenpoint. The value subtracted from y is the y-coordinate of thegiven point.
Reading the Lesson
1. In the formula y � y1 � m(x � x1), what do x1 and y1 represent?
x1 and y1 represent the coordinates of any given point on the graph of the line.
2. Complete the chart below by listing three forms of equations. Then write the formula foreach form. Finally, write three examples of equations in those forms.Sample examples are given.
Form of Equation Formula Example
slope-intercept y � mx � b y � 3x � 2
point-slope y � y1 � m(x � x1) y � 2 � 4(x � 3)
standard Ax � By � C 3x � 5y � 15
3. Refer to Example 5 on page 288 of your textbook. What do you think the hypotenuse of aright triangle is? Sample answers: The hypotenuse is the longest side ofthe right triangle. The hypotenuse is the side opposite the right angle ina right triangle.
Helping You Remember
4. Suppose you could not remember all three formulas listed in the table above. Which ofthe forms would you concentrate on for writing linear equations? Explain why you chosethat form. Sample answer: Point-slope form; the slope-intercept form can be written from the point-slope form. This is so because the y-intercept lets you write the coordinates of the point where the linecrosses the y-axis. You can use that point as the given point in the point-slope formula.
© Glencoe/McGraw-Hill 310 Glencoe Algebra 1
Collinearity You have learned how to find the slope between two points on a line. Doesit matter which two points you use? How does your choice of points affectthe slope-intercept form of the equation of the line?
1. Choose three different pairs of points from the graph at the right. Write the slope-intercept form of the line using each pair.
2. How are the equations related?
3. What conclusion can you draw from your answers to Exercises 1 and 2?
When points are contained in the same line, they are said to be collinear.Even though points may look like they form a straight line when connected,it does not mean that they actually do. By checking pairs of points on a line you can determine whether the line represents a linear relationship.
4. Choose several pairs of points from the graph at the right and write the slope-intercept form of the line using each pair.
5. What conclusion can you draw from your equations in Exercise 4? Is this a straight line?
x
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x
y
O
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-55-5
Study Guide and InterventionGeometry: Parallel and Perpendicular Lines
NAME ______________________________________________ DATE ____________ PERIOD _____
5-65-6
© Glencoe/McGraw-Hill 311 Glencoe Algebra 1
Less
on
5-6
Parallel Lines Two nonvertical lines are parallel if they have the same slope. All vertical lines are parallel.
Write the slope-intercept form for an equation of the line thatpasses through (�1, 6) and is parallel to the graph of y � 2x � 12.
A line parallel to y � 2x � 12 has the same slope, 2. Replace m with 2 and (x1, y1) with (�1, 6) in the point-slope form.y � y1 � m(x � x1) Point-slope form
y � 6 � 2(x � (�1)) m � 2; (x1, y1) � (�1, 6)
y � 6 � 2(x � 1) Simplify.
y � 6 � 2x � 2 Distributive Property
y � 2x � 8 Slope-intercept form
Therefore, the equation is y � 2x � 8.
Write the slope-intercept form for an equation of the line that passes through thegiven point and is parallel to the graph of each equation.
1. 2. 3.
4. (�2, 2), y � 4x � 2 5. (6, 4), y � x � 1 6. (4, �2), y � �2x � 3
7. (�2, 4), y � �3x � 10 8. (�1, 6), 3x � y � 12 9. (4, �6), x � 2y � 5
10. Find an equation of the line that has a y-intercept of 2 that is parallel to the graph ofthe line 4x � 2y � 8.
11. Find an equation of the line that has a y-intercept of �1 that is parallel to the graph ofthe line x � 3y � 6.
12. Find an equation of the line that has a y-intercept of �4 that is parallel to the graph ofthe line y � 6.
1�3
(–3, 3)
x
y
O
4x � 3y � –12
(–8, 7)
x
y
O
y � – 12x � 4
2
2
(5, 1)x
y
O
y � x � 8
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 312 Glencoe Algebra 1
Perpendicular Lines Two lines are perpendicular if their slopes are negativereciprocals of each other. Vertical and horizontal lines are perpendicular.
Write the slope-intercept form for an equation that passes through(�4, 2) and is perpendicular to the graph of 2x � 3y � 9.
Find the slope of 2x � 3y � 9.2x � 3y � 9 Original equation
�3y � �2x � 9 Subtract 2x from each side.
y � x � 3 Divide each side by �3.
The slope of y � x � 3 is . So, the slope of the line passing through (�4, 2) that is 2�3
2�3
2�3
Study Guide and Intervention (continued)
Geometry: Parallel and Perpendicular Lines
NAME ______________________________________________ DATE ____________ PERIOD _____
5-65-6
ExampleExample
ExercisesExercises
perpendicular to this line is the negative reciprocal of , or � .Use the point-slope form to find the equation.y � y1 � m(x � x1) Point-slope form
y � 2 � � (x � (�4)) m � � ; (x1, y1) � (�4, 2)
y � 2 � � (x � 4) Simplify.
y � 2 � � x � 6 Distributive Property
y � � x � 4 Slope-intercept form
Write the slope-intercept form for an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.
1. (4, 2), y � x � 1 2. (2, �3), y � � x � 4 3. (6, 4), y � 7x � 1
4. (�8, �7), y � �x � 8 5. (6, �2), y � �3x � 6 6. (�5, �1), y � x � 3
7. (�9, �5), y � �3x � 1 8. (�1, 3), 2x � 4y � 12 9. (6, �6), 3x � y � 6
10. Find an equation of the line that has a y-intercept of �2 and is perpendicular to thegraph of the line x � 2y � 5.
11. Find an equation of the line that has a y-intercept of 5 and is perpendicular to the graphof the line 4x � 3y � 8.
5�2
2�3
1�2
3�2
3�2
3�2
3�2
3�2
3�2
2�3
Skills PracticeGeometry: Parallel and Perpendicular Lines
NAME ______________________________________________ DATE ____________ PERIOD _____
5-65-6
© Glencoe/McGraw-Hill 313 Glencoe Algebra 1
Less
on
5-6
Write the slope-intercept form of an equation of the line that passes through thegiven point and is parallel to the graph of each equation.
1. 2. 3.
4. (3, 2), y � 3x � 4 5. (�1, �2), y � �3x � 5 6. (�1, 1), y � x � 4
7. (1, �3), y � �4x � 1 8. (�4, 2), y � x � 3 9. (�4, 3), y � x � 6
10. (4, 1), y � � x � 7 11. (�5, �1), 2y � 2x � 4 12. (3, �1), 3y � x � 9
Write the slope-intercept form of an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.
13. (�3, �2), y � x � 2 14. (4, �1), y � 2x � 4 15. (�1, �6), x � 3y � 6
16. (�4, 5), y � �4x � 1 17. (�2, 3), y � x � 4 18. (0, 0), y � x � 1
19. (3, �3), y � x � 5 20. (�5, 1), y � � x � 7 21. (0, �2), y � �7x � 3
22. (2, 3), 2x � 10y � 3 23. (�2, 2), 6x � 3y � �9 24. (�4, �3), 8x � 2y � 16
5�3
3�4
1�2
1�4
1�4
1�2
(–2, 2)
x
y
O
y � 12x � 1(1, –1)
x
y
O
y � –x � 3
(–2, –3)
x
y
O
y � 2x � 1
© Glencoe/McGraw-Hill 314 Glencoe Algebra 1
Write the slope-intercept form of an equation of the line that passes through thegiven point and is parallel to the graph of each equation.
1. (3, 2), y � x � 5 2. (�2, 5), y � �4x � 2 3. (4, �6), y � � x � 1
4. (5, 4), y � x � 2 5. (12, 3), y � x � 5 6. (3, 1), 2x � y � 5
7. (�3, 4), 3y � 2x � 3 8. (�1, �2), 3x � y � 5 9. (�8, 2), 5x � 4y � 1
10. (�1, �4), 9x � 3y � 8 11. (�5, 6), 4x � 3y � 1 12. (3, 1), 2x � 5y � 7
Write the slope-intercept form of an equation of the line that passes through thegiven point and is perpendicular to the graph of each equation.
13. (�2, �2), y � � x � 9 14. (�6, 5), x � y � 5 15. (�4, �3), 4x � y � 7
16. (0, 1), x � 5y � 15 17. (2, 4), x � 6y � 2 18. (�1, �7), 3x � 12y � �6
19. (�4, 1), 4x � 7y � 6 20. (10, 5), 5x � 4y � 8 21. (4, �5), 2x � 5y � �10
22. (1, 1), 3x � 2y � �7 23. (�6, �5), 4x � 3y � �6 24. (�3, 5), 5x � 6y � 9
25. GEOMETRY Quadrilateral ABCD has diagonals A�C� and B�D�.Determine whether A�C� is perpendicular to B�D�. Explain.
26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6).Determine whether triangle ABC is a right triangle. Explain.
x
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A
D
C
B
1�3
4�3
2�5
3�4
Practice Geometry: Parallel and Perpendicular Lines
NAME ______________________________________________ DATE ____________ PERIOD _____
5-65-6
Reading to Learn MathematicsGeometry: Parallel and Perpendicular Lines
NAME ______________________________________________ DATE______________ PERIOD _____
5-65-6
© Glencoe/McGraw-Hill 315 Glencoe Algebra 1
Less
on
5-6
Pre-Activity How can you determine whether two lines are parallel?
Read the introduction to Lesson 5-6 at the top of page 292 in your textbook.
• What is a family of graphs? A group of graphs that have at leastone characteristic in common, such as slope or y-intercept.
• Do you think lines that do not appear to intersect are parallel orperpendicular? parallel
Reading the Lesson
1. Refer to the Key Concept box on page 292. Why does the definition use the termnonvertical when talking about lines with the same slope? Vertical lines haveslopes that are undefined so we cannot say they have the same slope.
2. What is a right angle? Sample answers: A right angle is one that measures90°. It is an angle formed by perpendicular lines.
3. Refer to the Key Concept box on page 293. Describe how you find the opposite reciprocalof a number. Sample answer: The reciprocal of a given number is thenumber formed when you switch the numerator and denominator. Thenyou give it the opposite sign of the original number.
4. Write the opposite reciprocal of each number.
a. 2 � b. �3 c. � d. � 5
Helping You Remember
5. One way to remember how slopes of parallel lines are related is to say “same direction,same slope.” Try to think of a phrase to help you remember that perpendicular lineshave slopes that are opposite reciprocals.
Sample answer: Nicely right angles formed, use opposite reciprocals.
1�5
13�12
12�13
1�3
1�2
© Glencoe/McGraw-Hill 316 Glencoe Algebra 1
Pencils of LinesAll of the lines that pass through a single point in the same plane are called a pencil of lines.
All lines with the same slope,but different intercepts, are also called a “pencil,” a pencil of parallel lines.
Graph some of the lines in each pencil.
1. A pencil of lines through the 2. A pencil of lines described by point (1, 3) y � 4 � m(x � 2), where m is any
real number
3. A pencil of lines parallel to the line 4. A pencil of lines described by x � 2y � 7 y � mx � 3m � 2
x
y
Ox
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x
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Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-65-6
Study Guide and InterventionScatter Plots and Lines of Fit
NAME ______________________________________________ DATE ____________ PERIOD _____
5-75-7
© Glencoe/McGraw-Hill 317 Glencoe Algebra 1
Less
on
5-7
Interpret Points on a Scatter Plot A scatter plot is a graph in which two sets ofdata are plotted as ordered pairs in a coordinate plane. If y increases as x increases, there isa positive correlation between x and y. If y decreases as x increases, there is a negativecorrelation between x and y. If x and y are not related, there is no correlation.
EARNINGS The graph at the right shows the amount of money Carmen earned eachweek and the amount she deposited in her savingsaccount that same week. Determine whether thegraph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation, describe itsmeaning in the situation.
The graph shows a positive correlation. The more Carmen earns, the more she saves.
Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive correlation, describe it.
1. 2.
3. 4.Number of Mutual Funds
Years Since 1991
Nu
mb
er o
f Fu
nd
s(t
ho
usa
nd
s)
0 2 41 3 5 6 7
7
6
5
4
3
Source: The Wall Street Journal Almanac
Growth of Investment Clubs
Years Since 1990
Nu
mb
er o
f C
lub
s(t
ho
usa
nd
s)
0 2 41 3 5 6 7 8
35
28
21
14
7
Source: The Wall Street Journal Almanac
Average Jogging Speed
Minutes
Mile
s p
er H
ou
r
0 10 205 15 25
10
5
Average Weekly Work Hours in U.S.
Years Since 1990
Ho
urs
0 2 4 61 7 8 9 x
y
3 5
34.8
34.6
34.4
34.2
Source: The World Almanac
Carmen’s Earnings and Savings
Dollars Earned
Do
llars
Sav
ed
0 40 80 120
35
30
25
20
15
10
5
ExampleExample
ExercisesExercises
© Glencoe/McGraw-Hill 318 Glencoe Algebra 1
Lines of Fit
The table below shows the number of students per computer inUnited States public schools for certain school years from 1990 to 2000.
Year 1990 1992 1994 1996 1998 2000
Students per Computer 22 18 14 10 6.1 5.4
a. Draw a scatter plot and determine what relationship exists, if any.Since y decreases as x increases, the correlation is negative.
b. Draw a line of fit for the scatter plot.Draw a line that passes close to most of thepoints. A line of fit is shown.
c. Write the slope-intercept form of anequation for the line of fit.The line of fit shown passes through (1993, 16) and (1999, 5.7). Find the slope.
m �
m � �1.7
Find b in y � �1.7x � b.16 � �1.7 1993 � b
3404 � b Therefore, an equation of a line of fit is y � �1.7x � 3404.
Refer to the table for Exercises 1–3.
1. Draw a scatter plot. 3. Write the slope-intercept
2. Draw a line of fit for the data. form of an equation for theline of fit.
U.S. ProductionWorkers Hourly Wage
Years Since 1995
Ho
url
y W
age
(do
llars
)
0 1 32 4 5 6 7
14
13
12
11
Source: The World Almanac
Years Hourly Since 1995 Wage
0 $11.43
1 $11.82
2 $12.28
3 $12.78
4 $13.24
5.7 � 16��1999 � 1993
Students per Computerin U.S. Public Schools
Year
Stu
den
ts p
er C
om
pu
ter
1990 1992 1994 1996 1998 2000
24
20
16
12
8
4
0
Source: The World Almanac
Study Guide and Intervention (continued)
Scatter Plots and Lines of Fit
NAME ______________________________________________ DATE ____________ PERIOD _____
5-75-7
ExampleExample
ExercisesExercises
Skills PracticeStatistics: Scatter Plots and Lines of Fit
NAME ______________________________________________ DATE ____________ PERIOD _____
5-75-7
© Glencoe/McGraw-Hill 319 Glencoe Algebra 1
Less
on
5-7
Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation,describe its meaning in the situation.
1. 2.
3. 4.
BASEBALL For Exercises 5–7, use the scatterplot that shows the average price of a major-league baseball ticket from 1991 to 2000.
5. Determine what relationship, if any, exists in the data. Explain.
6. Use the points (1993, 9.60) and (1998, 13.60) to write the slope-intercept form of an equationfor the line of fit shown in the scatter plot.
7. Predict the price of a ticket in 2004.
Baseball Ticket Prices
Year
Ave
rag
e Pr
ice
($)
’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99
18
16
14
12
10
8
0’00
Source: Team Marketing Report, Chicago
Evening Newspapers
Year
Nu
mb
er o
f N
ewsp
aper
s
’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99
1050
1000
950
900
850
800
750
0
Source: Editor & Publisher
Weight-Lifting
Weight (pounds)
Rep
etit
ion
s
0 40 8020 60 100120140
14
12
10
8
6
4
2
Library Fines
Books Borrowed
Fin
es (
do
llars
)
0 2 4 5 6 7 8 81 3 10
7
6
5
4
3
2
1
Calories BurnedDuring Exercise
Time (minutes)
Cal
ori
es
0 20 4010 30 50 60
600
500
400
300
200
100
© Glencoe/McGraw-Hill 320 Glencoe Algebra 1
Determine whether each graph shows a positive correlation, a negativecorrelation, or no correlation. If there is a positive or negative correlation,describe its meaning in the situation.
1. 2.
DISEASE For Exercises 3–6, use the table that shows the number of cases of mumps in the United States for the years 1995 to 1999.
3. Draw a scatter plot and determine what relationship, if any, exists in the data.
Source: Centers for Disease Control and Prevention
4. Draw a line of fit for the scatter plot.
5. Write the slope-intercept form of an equation for theline of fit.
6. Predict the number of cases in 2004.
ZOOS For Exercises 7–10, use the table that shows the average and maximum longevity ofvarious animals in captivity.
7. Draw a scatter plot and determine what relationship, if any, exists in the data. Source: Walker’s Mammals of the World
8. Draw a line of fit for the scatter plot.
9. Write the slope-intercept form of an equation for the line of fit.
10. Predict the maximum longevity for an animal with an average longevity of 33 years.
Longevity (years)
Avg. 12 25 15 8 35 40 41 20
Max. 47 50 40 20 70 77 61 54
U.S. Mumps Cases
Year
Cas
es
1995 1997 1999 2001
1000
800
600
400
200
0
U.S. Mumps Cases
Year 1995 1996 1997 1998 1999
Cases 906 751 683 666 387
State Elevations
Mean Elevation (feet)
Hig
hes
t Po
int
(th
ou
san
ds
of
feet
)
10000 2000 3000
16
12
8
4
Source: U.S. Geological Survey
Temperature versus Rainfall
Average Annual Rainfall (inches)
Ave
rag
eTe
mp
erat
ure
(�F
)
10 15 20 25 30 35 40 45
64
60
56
52
0
Source: National Oceanic and Atmospheric Administration
Practice Statistics: Scatter Plots and Lines of Fit
NAME ______________________________________________ DATE ____________ PERIOD _____
5-75-7
Reading to Learn MathematicsStatistics: Scatter Plots and Lines of Fit
NAME ______________________________________________ DATE______________ PERIOD _____
5-75-7
© Glencoe/McGraw-Hill 321 Glencoe Algebra 1
Less
on
5-7
Pre-Activity How do scatter plots help identify trends in data?
Read the introduction to Lesson 5-7 at the top of page 298 in your textbook.
• What does the phrase linear relationship mean to you? Sampleanswer: It means that when you graph the data points on acoordinate grid, the points all lie on or close to a line thatyou could draw on the grid.
• Write three ordered pairs that fit the description as x increases, ydecreases. Sample answer: {(2, 5), (3, 3), (4, 1)}
Reading the Lesson
1. Look up the word scatter in a dictionary. How does this definition compare to the termscatter plot? One definition states “to occur or fall irregularly or atrandom.”The points in a scatter plots usually do not follow an exactlinear pattern, but fall irregularly on the coordinate plane.
2. What is a line of fit? How many data points fall on the line of fit? A line of fit showsthe trend of the data. It is impossible to say how many data points mayfall on a line of fit—maybe several, maybe none.
3. What is linear interpolation? How can you distinguish it from linear extrapolation?Linear interpolation is the process of predicting a y-value for a given x-value that lies between the least and greatest x-values in the data set.“Inter-” means between and “extra-” means beyond. If the x-value isbetween the extremes of the x-values in the data set, you sayinterpolation; if the x-value is less than or greater than the extremes,you say extrapolation.
Helping You Remember
4. How can you remember whether a set of data points shows a positive correlation or anegative correlation? If it looks like a line of fit for the points would have apositive slope, there is a positive correlation. If it looks like a line of fitwould have a negative slope, there is a negative correlation.
© Glencoe/McGraw-Hill 322 Glencoe Algebra 1
Latitude and Temperature The latitude of a place on Earthis the measure of its distancefrom the equator. What do youthink is the relationship between a city’s latitude and its January temperature? At the right is a table containing the latitudes and January mean temperatures for fifteenU.S. cities.
Sources: www.indo.com and www.nws.noaa.gov/climatex.html
1. Use the information in the table to create a scatter plot and draw a line of best fit for the data.
2. Write an equation for the line of fit. Make a conjecture about the relationship between a city’s latitude and its meanJanuary temperature.
3. Use your equation to predict the Januarymean temperature of Juneau, Alaska,which has latitude 58:23 N.
4. What would you expect to be the latitude of a city with a January mean temperature of 15°F?
5. Was your conjecture about the relationship between latitude and temperature correct?
6. Research the latitudes and temperatures for cities in the southern hemisphere instead.Does your conjecture hold for these cities as well?
Latitude (�N)
Tem
per
atu
re (
�F)
70
60
50
40
30
20
10
0
�10
T
L20 40 6010 30 50
U.S. City Latitude January Mean Temperature
Albany, New York 42:40 N 20.7°F
Albuquerque, New Mexico 35:07 N 34.3°F
Anchorage, Alaska 61:11 N 14.9°F
Birmingham, Alabama 33:32 N 41.7°F
Charleston, South Carolina 32:47 N 47.1°F
Chicago, Illinois 41:50 N 21.0°F
Columbus, Ohio 39:59 N 26.3°F
Duluth, Minnesota 46:47 N 7.0°F
Fairbanks, Alaska 64:50 N �10.1°F
Galveston, Texas 29:14 N 52.9°F
Honolulu, Hawaii 21:19 N 72.9°F
Las Vegas, Nevada 36:12 N 45.1°F
Miami, Florida 25:47 N 67.3°F
Richmond, Virginia 37:32 N 35.8°F
Tucson, Arizona 32:12 N 51.3°F
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
5-75-7
Chapter 5 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 323 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.For Questions 1–4, find the slope of each line described.
1. the line through (3, 7) and (�1, 4)
A. �43� B. �
34� C. �
121� D. �1
21�
1.
2. the line through (�3, 2) and (6, 2)
A. �49� B. �
43� C. 0 D. undefined 2.
3. the line graphed at the right
A. �23� B. �
32�
C. ��32� D. ��
23� 3.
4. a vertical lineA. 1 B. 0 C. �1 D. undefined 4.
5. Which graph has a slope of �3?A. B. C. D. 5.
6. COMMUNICATION In 1996, there were 171 area codes in the United States.In 1999, there were 285. Find the rate of change from 1996 to 1999.
A. 114 B. 38 C. �318�
D. �144 6.
For Questions 7–9, find the equation in slope-intercept form that describes each line.
7. a line through (2, 4) with slope 0A. y � 2 B. x � 2 C. y � 4 D. x � 4 7.
8. a line through (4, 2) with slope �12�
A. y � ��12�x B. y � �
12�x � 4 C. y � 2x � 10 D. y � �
12�x 8.
9. a line through (�1, 1) and (2, 3)
A. y � �23�x � �
53� B. y � ��
23�x � �
53� C. y � �
23�x � �
53� D. y � ��
23�x � �
53� 9.
10. If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost?A. $37.75 B. $29.75 C. $47.60 D. $0.16 10.
11. What is the standard form of y � 8 � 2(x � 3)?A. 2x � y � 14 B. y � 2x � 14 C. 2x � y � �14 D. y � 2x � 11 11.
y
xO
y
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y
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y
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(3, 1)
(0, �1)
© Glencoe/McGraw-Hill 324 Glencoe Algebra 1
Chapter 5 Test, Form 1 (continued)
12. Which is the graph of y � ��34�x?
A. B. C. D. 12.
13. Which is the point-slope form of an equation for the line that passes through (0, �5) with slope 2?A. y � 2x � 5 B. y � 5 � 2x C. y � 5 � x � 2 D. y � 2(x � 5) 13.
14. What is the slope-intercept form of y � 6 � 2(x � 2)?A. y � 2x � 6 B. y � 2x � 2 C. y � 2x � 6 D. 2x � y � 6 14.
15. When are two lines parallel?A. when the slopes are opposite B. when the slopes are equalC. when the product of the slopes is 1 D. when the slopes are positive 15.
16. Find the slope-intercept form of an equation for the line that passes through (�1, 2) and is parallel to y � 2x � 3.A. y � 2x � 4 B. y � 0.5x � 4 C. y � 2x � 3 D. y � �0.5x � 4 16.
17. Find the slope-intercept form of an equation of the line perpendicular to the graph of x � 3y � 5 and passing through (0, 6).
A. y � �13�x � 2 B. y � �3x � 6 C. y � �
13�x � 2 D. y � 3x � 6 17.
For Questions 18 and 19, use the scatter plot at the right.
18. How would you describe the relationship between the x and y values in the scatter plot?A. strong negative correlationB. weak negative correlationC. weak positive correlationD. strong positive correlation 18.
19. Based on the data in the scatter plot, what would you expect the y value to be for x � 2010?A. greater than 80 B. between 80 and 65C. between 65 and 50 D. less than 50 19.
20. What is an equation of the line whose graph has slope of 2 and a y-intercept of �5?A. y � �5x � 2 B. y � 5x � 2 C. y � 2x � 5 D. y � 2x � 5 20.
Bonus Find the value of r in (4, r), (r, 2) so that the slope of the
line containing them is ��53�. B:
y
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y
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50
60
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90
'80 '85 '90 '95 '00
Chapter 5 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 325 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.
1. What is the slope of the line through (1, 9) and (�3, 16)?
A. ��74� B. ��
47� C. ��
225� D. ��2
25�
1.
2. What is the slope of the line through (�4, 3) and (5, 3)? A. 0 B. undefined C. 9 D. 1 2.
3. Find the value of r so that the line through (8, r) and (4, 5) has a slope of �4.A. 11 B. �11 C. 4 D. �4 3.
4. In 1995, there were 12,000 students at Beacon High. In 2000, there were 12,250. What is the rate of change in the number of students?A. 250/yr B. 50/yr C. 42/yr D. 200/yr 4.
5. Which is the graph of y � �23�x?
A. B. C. D. 5.
6. If y varies directly as x and y � 3 when x � 10, find x when y � 8.
A. �830� B. �
152� C. �
145� D. none of these 6.
7. A driver’s distance varies directly as the amount of time traveled. After 6 hours, a driver had traveled 390 miles. How far had the driver traveled after 4 hours?A. 130 miles B. 220 miles C. 260 miles D. 650 miles 7.
8. A line of fit might be defined asA. a line that connects all the data points.B. a line that might best estimate the data and be used for predicting values.C. a vertical line halfway through the data.D. a line whose slope is greater than 1. 8.
9. What is the slope-intercept form of the equation of a line with slope 5 and y-intercept �8?A. y � �8x � 5 B. y � 8x � 5 C. 5x � y � � 8 D. y � 5x � 8 9.
10. Which equation is graphed at the right?A. 2y � x �10 B. 2x � y � �5C. 2x � y � 5 D. 2y � x � �5 10.
11. Which is an equation of the line that passes through (2, �5) and (6, 3)?
A. y � �12�x � 6 B. y � �
12�x
C. y � 2x � 12 D. y � 2x � 9 11.
O
y
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y
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y
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y
x
55
y
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© Glencoe/McGraw-Hill 326 Glencoe Algebra 1
Chapter 5 Test, Form 2A (continued)
12. What is the standard form of the equation of the line through (0, �3) with
slope �25�?
A. �5x � 2y � 15 B. �5x � 2y � �15C. 2x � 5y � 15 D. �2x � 5y � 15 12.
13. Which is an equation of the line with slope �3 and a y-intercept of 5?A. y � �3(x � 5) B. y � 5 � �3x C. �3x � y � 5 D. y � 5x � 3 13.
14. What is the standard form of y � 7 � ��23�(x �1)?
A. �2x � 3y � 23 B. �3x � 2y � 17 C. 2x � 3y � 19 D. 3x � 2y � 11 14.
15. What is the equation of the line through (�2, �3) with a slope of 0?A. x � �2 B. y � �3 C. �2x � 3y � 0 D. �3x � 2y � 0 15.
16. Find the slope-intercept form of the equation of the line that passes through (�5, 3) and is parallel to 12x � 3y � 10.A. y � �4x � 17 B. y � 4x � 13 C. y � � 4x � 13 D. y � 4x � 23 16.
17. If line q has a slope of ��38�, what is the slope of any line perpendicular to q?
A. ��38� B. �
38� C. �
83� D. ��
83� 17.
For Questions 18 and 19, use the scatter plot at the right.
18. Which data are shown by the scatter plot?A. (1980, 5.5), (1982, 6.1), (1989, 7.6)B. (1980, 5.5), (1985, 6.1), (1989, 7.6)C. (1980, 5.5), (1985, 6.6), (1990, 8.0)D. (1980, 5.5), (1982, 6.6), (1990, 8.0) 18.
19. Based on the data in the scatter plot, what would you expect the y value to be for x � 1995?A. between 7 and 8 B. higher than 8C. between 5 and 7 D. impossible to tell 19.
20. To calculate the charge for a load of bricks, including delivery, the Redstone Brick Co. uses the equation C � 0.42b � 25, where C is the charge and b is the number of bricks. What is the delivery fee per load?A. $42 B. $67C. $25 D. It depends on the number of bricks 20.
Bonus What is the y-intercept of a line through (2, 7) and
perpendicular to the line y � ��32�x � 6? B:
NAME DATE PERIOD
55
0
5
6
7
8
'80 '85 '90
Chapter 5 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 327 Glencoe Algebra 1
Ass
essm
ent
Write the letter for the correct answer in the blank at the right of each question.1. What is the slope of the line through (2, �8) and (4, 1)?
A. ��29� B. ��
67� C. ��
76� D. �
92� 1.
2. What is the slope of the line through (�4, �6) and (9, �6)?
A. ��152� B. ��1
52�
C. 0 D. undefined 2.
3. Find the value of r so that the line through (8, 5) and (4, r) has a slope of �4.A. 21 B. �21 C. 11 D. �11 3.
4. In 1995, MusicMart sold 12,000 CDs. In 2000, they sold 14,550 CDs. What is the rate of change in the number of CDs sold?A. 2550/yr B. 510/yr C. 425/yr D. 2400/yr 4.
5. Which is the graph of y � ��12�x?
A. B. C. D. 5.
6. If y varies directly as x and y � 5 when x � 8, find y when x � 9.
A. �752� B. �
485� C. �
490� D. 6 6.
7. The amount a spring stretches varies directly as the weight of the object attached to it. If an 8-ounce weight stretches a spring 10 centimeters, how much weight will stretch it 15 centimeters?A. 16 oz B. 6 oz C. 10 oz D. 12 oz 7.
8. The graph of data that has a strong negative correlation has A. a narrow linear pattern from lower left to upper right.B. a narrow linear pattern from upper left to lower right.C. a narrow horizontal pattern below the x-axis.D. all negative x-values. 8.
9. What is the slope-intercept form of the equation of the line with slope �14�
and y-intercept at the origin?
A. y � 4x B. y � �14�x C. y � x � �
14� D. y � �
14� � x 9.
10. Which equation is graphed at the right?A. y � 2x � �4 B. 2x � y � �4C. 2x � y � 4 D. y �4 � 2x 10.
11. Which is an equation of the line that passes through (4, �5) and (6, �9)?
A. y � �12�x � 3 B. y � �
12�x � 3 C. y � �2x � 3 D. y � 2x � 3 11.
O
y
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y
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y
x
y
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55
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y
x
© Glencoe/McGraw-Hill 328 Glencoe Algebra 1
Chapter 5 Test, Form 2B (continued)
12. What is the standard form of the equation of the line through (6, �3) with
slope �23�?
A. �2x � 3y � 24 B. 2x � 3y � 21 C. 3x � 2y � 24 D. 3x � 2y � �21 12.
13. Which is an equation of the line with slope �3 that passes through (2, 4)?A. y � 4 � �3(x � 2) B. y � 4 � �3x � 2C. y � 4 � �3(x � 2) D. y �2 � �3(x � 4) 13.
14. What is the standard form of y � 2 � �12�(x � 4)?
A. x � 2y � 0 B. x � 2y � 8 C. 2x � y � 10 D. 4x � 2y � 0 14.
15. What is the equation of the line through (�2, �3) with an undefined slope?A. x � �2 B. y � �3 C. �2x � 3y � 0 D. �3x � 2y � 0 15.
16. Find the slope-intercept form of the equation of the line that passes through (�1, 5) and is parallel to 4x � 2y � 8.A. y � �2x � 9 B. y � 2x � 9 C. y � 4x � 9 D. y � �2x � 3 16.
17. If line q has a slope of �2, what is the slope of any line perpendicular to q?
A. 2 B. �2 C. �12� D. ��
12� 17.
For Questions 18 and 19, use the scatter plot at the right.
18. Which data are shown by the scatter plot?A. (1970, 47), (1980, 31), (1986, 24)B. (1970, 50), (1985, 25), (1990, 0)C. (47, 1970), (31, 1980), (24, 1986)D. (1976, 45), (1980, 35), (1985, 8) 18.
19. Based on the data in the scatter plot,which statement is true?A. As x increases, y increases.B. As x increases, y decreases.C. There is no relationship between x and y.D. There are not enough data to determine the relationship between x and y. 19.
20. A baby blue whale weighed 3 tons at birth. Ten days later, it weighed 4 tons. Assuming the same rate of growth, which equation shows the weight w when the whale is d days old?A. w � 10d � 3 B. w � 10d � 4 C. w � 0.1d � 3 D. w � d � 10 20.
Bonus For what value of k does kx � 7y � 10 have a slope of 3? B:
NAME DATE PERIOD
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30
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'70 '80 '90
Chapter 5 Test, Form 2C
© Glencoe/McGraw-Hill 329 Glencoe Algebra 1
For Questions 1–3, find the slope of the line passing through each pair of points.If the slope is undefined, write “undefined.”
1. (2, 5) and (3, 6) 1.
2. (�1, 3) and (6, 3) 2.
3. (6, �4) and (�3, 7) 3.
4. Find the value of r so that the line through (�4, 8) and 4.
(r, �6) has a slope of �23�.
5. In 1968, vehicle emission standards allowed 5.6.3 hydrocarbons released per mile driven. By 1980, the standards allowed only 0.41 hydrocarbons per mile driven.What was the rate of change from 1968 to 1980?
6. Graph y � ��12�x. 6.
7. If a shark can swim 27 miles in 9 hours, how many miles 7.will it swim in 12 hours?
8. Write a linear equation in slope-intercept form to model the 8.situation: A telephone company charges $28.75 per month plus 10¢ a minute for long-distance calls.
9. Write an equation in standard form of the line that passes 9.through (7, �3) and has a y-intercept of 2.
10. Write the slope-intercept form of an 10.equation for the line graphed at the right.
11. Graph the line with y-intercept 3 and 11.
slope ��34�.
y
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y
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© Glencoe/McGraw-Hill 330 Glencoe Algebra 1
Chapter 5 Test, Form 2C (continued)
12. Write an equation in slope-intercept form for the line that 12.passes through (�1, �2) and (3, 4).
13. Write an equation in standard form for the line whose slope 13.is undefined and passes through (�6, 4).
14. Write an equation in point-slope form for the line that has 14.
slope �13� and passes through (�2, 8).
15. Write the standard form of the equation y � 4 � ��172�(x � 1). 15.
16. Write the slope-intercept form of the equation 16.y � 2 � 3(x � 4).
17. Write the slope-intercept form of the equation of the line 17.parallel to the graph of 2x � y � 5 that passes through (0, 1).
18. Write the slope-intercept form of the equation of the line 18.
perpendicular to the graph of y � ��32�x � 7 that passes
through (3, �2).
For Questions 19 and 20, use the data in the table.
19. Make a scatter plot relating time spent studying to the 19.score received.
20. Write the slope-intercept form of the equation for a line 20.of fit for the data. Use your equation to predict a student’s score if the student spent 35 minutes studying.
Bonus In a certain lake, a 1-year-old bluegill fish is 3 inches B:long, while a 4-year-old bluegill fish is 6.6 inches long.Assuming the growth rate can be approximated by a linear equation, write an equation in slope-intercept form for the length � of a bluegill fish in inches after t years. Then use the equation to determine the age of a 9-inch bluegill.
Time Spent Studying(minutes)
Sco
re R
ecei
ved
(per
cen
t)
0
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100
10 20 30 40 50
NAME DATE PERIOD
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Time Spent Studying (min) 10 20 30 40 50
Score Received (percent) 53 67 78 87 95
Chapter 5 Test, Form 2D
© Glencoe/McGraw-Hill 331 Glencoe Algebra 1
For Questions 1–3, find the slope of the line passing through each pair of points.If the slope is undefined, write “undefined.”
1. (4, 1) and (�4, 1) 1.
2. (�2, 1) and (3, �2) 2.
3. (�6, 7) and (�6, �2) 3.
4. Find the value of r so that the line through (4, 5) and 4.
(r, 3) has a slope of �23�.
5. In 1983, 57.5% of college students graduated in 5 or fewer 5.years of study. In 1997, that number had fallen to 52.8%.What was the change of rate for percent of students graduating within 5 years from 1983 to 1997?
6. Graph y � �23�x. 6.
7. If a snail travels 200 inches in 2 hours, how long will it take 7.the snail to travel 50 inches?
8. Write a linear equation in slope-intercept form to model 8.the situation: An Internet company charges $4.95 per month plus $2.50 for each hour of use.
9. Write an equation in standard form of the line that passes 9.through (3, 1) and has a y-intercept of �2.
10. Write the slope-intercept form 10.of an equation for the line graphed at the right.
11. Graph the line with y-intercept 2 11.
and slope ��12�.
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y
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© Glencoe/McGraw-Hill 332 Glencoe Algebra 1
Chapter 5 Test, Form 2D (continued)
12. Write an equation in slope-intercept form for the line that 12.passes through (5, 4) and (6, �1).
13. Write an equation in standard form for the line whose slope 13.is undefined that passes through (5, �3).
14. Write an equation in point-slope form for the line that has 14.
slope �43� and passes through (3, 0).
15. Write the standard form of the equation y � 3 � ��23�(x � 5). 15.
16. Write the slope-intercept form of the equation 16.
y � 1 � �34�(x � 3).
17. Write the slope-intercept form of the equation of the line 17.parallel to the graph of 9x � 3y � 6 that passes through (5, 3).
18. Write the slope-intercept form of the equation of the line 18.perpendicular to the graph of 4x � y � 12 that passes through (8, 2).
For Questions 19 and 20, use the data that shows age and percent of budget spent on entertainment in the table.
19. Make a scatter plot relating the age to the percent of the 19.person’s budget spent on entertainment.
20. Write the slope-intercept form of the equation for a line 20.of fit for the data. Use your equation to predict the percent of a 65-year-old person’s budget.
Bonus Write an equation in slope-intercept form of the line B:with y-intercept �6 and parallel to a line perpendicular to 5x � 6y � 13 � 0.
Age
Perc
ent
Spen
t o
nEn
tert
ain
men
t
3
4
5
6
30 40 50 60 70 80
NAME DATE PERIOD
55
Age 30 40 50 60 70 80
Percent Spent on Entertainment 6.1 6.0 5.4 5.0 4.7 3.4
Chapter 5 Test, Form 3
© Glencoe/McGraw-Hill 333 Glencoe Algebra 1
For Questions 1 and 2, find the slope of the line passing through each pair ofpoints. If the slope is undefined, write “undefined.”
1. (�8, 7) and (5, �2) 1.
2. (5, 9) and (5, �3) 2.
3. Find the value of r so that the line through (�4, 3) and (r, �3) 3.
has a slope of �23�.
4. Find the value of r so that the line through (r, 5) and (6, r) 4.
has a slope of �58�.
5. In 1990, there were approximately 35,000 people in 5.Lancaster. Five years later, the population was 38,452.Find the rate of change in the population.
6. Graph y � ��34�x. 6.
7. If an ostrich can run 15 kilometers in 15 minutes, how 7.many kilometers can it run in an hour?
8. Write the point-slope form of an equation of the line that has 8.
slope ��35� and passes through (2, 1).
9. Write an equation in standard form of the line that passes 9.through (2, �3) and (�3, 7).
10. Graph a line whose x-intercept is 5 and whose slope is ��35�. 10.
11. Write y � 4 � ��23�(x � 9) in standard form. 11.
12. Write the point-slope form of the equation for the line that 12.has x-intercept �3 and y-intercept �2.
y
xO
y
xO
NAME DATE PERIOD
SCORE 55
Ass
essm
ent
© Glencoe/McGraw-Hill 334 Glencoe Algebra 1
Chapter 5 Test, Form 3 (continued)
For Questions 13–20, write an equation in slope-intercept form of the linesatisfying the given conditions.
13. has y-intercept �8 and slope 3 13.
14. has slope �52� and passes through (4, �1) 14.
15. passes through (�3, 7) and (2, 4) 15.
16. is horizontal and passes through (�4, 6) 16.
17. is parallel to the y-axis and has an x-intercept of 3 17.
18. is perpendicular to 4y � 3x � 8 and passes through (�12, 7) 18.
19. is parallel to 3x � 5y � 7 and passes through (0, �6) 19.
20. is perpendicular to the y-axis and passes through (�2, 5) 20.
For Questions 21–23, use the data in the table.
21. Make a scatter plot relating the verbal scores and the 21.math scores.
22. Does the scatter plot in Question 21 show a positive, a 22.negative, or no correlation? What does that relationship represent?
23. Write the equation for a line of fit. Predict the 23.corresponding math score for a verbal score of 445.
24. A rental car company charges $52.99 per day, including 200 24.free kilometers. There is a charge of $0.12/km for additional kilometers. Write a linear equation that models this situation.
25. Write the slope-intercept form of y � 3 � �0.5(x � 10). 25.
Bonus The area of a circle varies directly as the square of the B:radius. If the radius is tripled, by what factor will the area increase?
Verbal Score
Mat
h S
core
450
460
470
480
490
500
400420440460480
NAME DATE PERIOD
55
State Graduation Scores
Year Verbal Score Math Score1970 460 488
1980 424 466
1990 410 463
2000 420 460
Chapter 5 Open-Ended Assessment
© Glencoe/McGraw-Hill 335 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.
1. Draw a line on a coordinate plane so that you can determine atleast two points on the graph.a. Describe how you would determine the slope of the graph and
justify the slope you found.b. Explain how you could use the slope to write various forms
of the equation of that line. Then write three forms of the equation.
2. You are told that a line passes through (�2, 3).a. Discuss what other information you would need to graph this
line.b. Then describe how you would use that information to graph
the line and write its equation.
3. Refer to the scatter plot at the right.a. Describe the pattern of points in the
scatter plot and the relationship between x and y.
b. Give at least two examples of real-life situations that, if graphed, would result in a correlation like the one shown in this scatter plot.
c. Add a scale and heading to each axis. Then write an equationthat would model the points represented by this plot.
4. The table gives the life expectancy of a child born in the United States in a given year.a. Make a scatter plot of the data.b. Can you use the data to claim
that the increase in life expectancy is due to improved health care? Explain your response.
c. Use the data to predict the life expectancy of a baby born in 2000. Explain how you determined your answer.
Source: National Center for Health Statistics
NAME DATE PERIOD
SCORE 55
Ass
essm
ent
y
xO
Years of Life Expected at Birth
Year ofBirth
Life Expectancy(years)
1920 54.1
1930 59.7
1940 62.9
1950 68.2
1960 69.7
1970 70.8
1980 73.7
1985 74.7
1990 75.4
1995 75.8
© Glencoe/McGraw-Hill 336 Glencoe Algebra 1
Chapter 5 Vocabulary Test/Review
Choose from the terms above to complete each sentence.
1. If two lines have slopes that are negative reciprocals of each other,
then they are . If they have slopes that
are the same, then they are .
2. In the equation, y � kx, k represents the .
3. A graph of data points is sometimes called a .
4. Several graphs who have one or more common characteristics form a
.
5. Earning $7.50 per hour is an example of a .
6. The leftmost data point in a set is (3, 27) and the rightmost point is (12, 13). If you use a linear prediction equation to find thecorresponding y value for x � 10, you are using a method called
.
7. The ratio of the rise to the run or the ratio of the change in the y-coordinates to the change in the x-coordinates are definitions of
.
8. The equation y � �3x � 12 is written in form.
9. The equation y � 6 � 2(x � 4) is written in form.
10. The equation 3x � y � 12 is written in form.
In your own words—Define each term.
11. line of fit
12. linear extrapolation
best-fit lineconstant of variationdirect variationfamily of graphslinear extrapolation
linear interpolationline of fitnegative correlationparallel linesperpendicular lines
point-slope formpositive correlationrate of changescatter plot
slopeslope-intercept formstandard form
NAME DATE PERIOD
SCORE 55
Chapter 5 Quiz (Lessons 5–1 and 5–2)
55
© Glencoe/McGraw-Hill 337 Glencoe Algebra 1
Determine the slope of the line passing through each pair of points.
1. (5, 8) and (�4, 6) 1.
2. (9, 4) and (5, �3) 2.
3. (�3, 10) and (�3, 6) 3.
4. In 1996, there were approximately 275 students in the 4.Delaware High School band. In 2002, that number increased to 305. Find the annual rate of change in the number of students in the band.
5. Chris’s wages vary directly as the time she works. If her 5.wages for 20 hours are $150, what are her wages for 38 hours?
NAME DATE PERIOD
SCORE
Chapter 5 Quiz (Lessons 5–3 and 5–4)
Write the slope-intercept form of the equation for each situation.
1. slope: �14�, y-intercept: �5 1.
2. line passing through (9, 2) and (�2, 6) 2.
3. Graph 4x � 3y � 12. 3.
4. Write a linear equation in slope-intercept form to model a tree 4 feet tall that grows 3 inches per year. 4.
5. STANDARDIZED TEST PRACTICE The table of ordered pairs shows the coordinates of the two points on the graph of a function. Which equation describes the function?
A. y � �2x � 1 B. y � �12�x � 1
C. y � ��12�x � 1 D. y � ��
12�x � 1 5.
y
xO
NAME DATE PERIOD
SCORE 55
Ass
essm
ent
x y
�2 2
4 �1
© Glencoe/McGraw-Hill 338 Glencoe Algebra 1
1. Write the point-slope form of an equation for a line passing 1.
through (3, 6) with slope m � ��13�.
2. Write y � 9 � �(x � 2) in slope-intercept form. 2.
3. Write the point-slope form of an equation for the horizontal 3.line that passes through (�4, �1).
4. Write the slope-intercept form of an equation for the line 4.that passes through (5, 3) and is parallel to x � 3y � 6.
5. Write the slope-intercept form of an equation for the line 5.that passes through (0, 3) and is perpendicular to 9x � 4y � �8.
Chapter 5 Quiz (Lesson 5–7)
1. Use the data in the table to make a scatter plot relating 1–2.age to median income.
2. Draw a fit line for the scatter plot.
3. Do the data show a positive or negative relationship? What 3.does this relationship mean?
4. Write the slope-intercept form of an equation for a line of fit. 4.
5. Use the line of fit to predict the median income for someone 5.32 years old.
Age
Med
ian
Inco
me
($10
00)
16
19
22
25
28
31
26 27 28 29 30
NAME DATE PERIOD
SCORE
Chapter 5 Quiz (Lessons 5–5 and 5–6)
55
NAME DATE PERIOD
SCORE
55
Age 26 27 28 29 30
Median Income($1000) 16.8 19.1 23.3 25.8 33.9
Chapter 5 Mid-Chapter Test (Lessons 5–1 through 5–4)
© Glencoe/McGraw-Hill 339 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. Find the slope of the line through (6, �7) and (4, �8).
A. ��12� B. 2 C. �
12� D. �2 1.
2. Find the slope of the line through (0, 5) and (5, 5).A. 0 B. 1 C. 2 D. no slope 2.
3. In 1999, 96.60 quadrillion Btu (British thermal units) of energy were consumed in the United States. In 1995, 90.86 quadrillion Btu were consumed. Which of the following is the rate of change in consumption from 1995 to 1999?A. 1.44 quadrillion btu per yearB. 5.74 quadrillion btu per yearC. 0.69 years per quadrillion btuD. 0.57 quadrillion btu per year 3.
4. The total price of a bag of peaches varies directly with the cost per pound.If 3 pounds of peaches cost $3.60, how much would 5.5 pounds cost?A. $1.20 B. $6.60 C. $6.00 D. $1.96 4.
5. Which is the slope-intercept form of an equation for the line containing (0, �3) with slope �1?A. y � �x � 3 B. y � �3x � 1 C. y � x � 3 D. x � �3y � 1 5.
For Questions 6–8, write an equation in slope-intercept form of the line satisfying the given conditions.
6. has y-intercept 5 and slope ��34� 6.
7. passes through (4, 2) and (0, �2) 7.
8. has slope �3 and passes through (2, �4) 8.
For Questions 9 and 10, use the graph at the right.
9. What is the slope of the line shown 9.in the graph?
10. What is the equation of the line 10.shown in the graph?
Part II
Part I
NAME DATE PERIOD
SCORE 55
Ass
essm
ent
y
xO
P (2, 0)
© Glencoe/McGraw-Hill 340 Glencoe Algebra 1
Chapter 5 Cumulative Review (Chapters 1–5)
1. Write 2 � r � r � s � s using exponents. (Lesson 1-1) 1.
2. Evaluate 2xy � y2 if x � 6 and y � 12. (Lesson 1-2) 2.
Simplify each expression. (Lessons 2-3 through 2-5)
3. 4�78� � 2�
58� 4. �
38� � 2�1
78�
5. ��23� � �
34� 6. �3.9 � (�2.5) � (�8.7)
7. 4(2y � y) � 6(4y � 3y) 8. �12a��618b
�
For Questions 9–11, solve each equation. (Lessons 3-2 through 3-4)
9. 13 � m � 21 9.
10. �34�x � �
23� 10.
11. 4x � 12 � �16 11.
12. Solve x � 2y � 12 if the domain is {�3, �1, 0, 2, 5}. 12.(Lesson 4-4)
13. Determine whether {(1, 4), (2, 6), (3, 7), (4, 4)} is a function, 13.and explain your reasoning. (Lesson 4-6)
14. Write an equation for the relationship between the variables 14.in the chart. (Lesson 4-8)
15. Determine the slope of the line passing through (2, 7) and 15.(�5, 2). (Lesson 5-1)
16. Write an equation in slope-intercept form for the line 16.passing through (2, 6) with slope �3. (Lesson 5-3)
17. Write an equation for the line passing through (�6, 5) and 17.(�6, �4). (Lesson 5-4)
18. Write the slope-intercept form of an equation for the line 18.that is parallel to 5x � 3y � 1 and passes through (0, �4).(Lesson 5-6)
NAME DATE PERIOD
55
3.
4.
5.
6.
7.
8.
x 0 2 4 6
y 2 5 8 11
© Glencoe/McGraw-Hill 341 Glencoe Algebra 1
1. If a � 2, b � 6, and c � 4, then �(4ba
��
cb)2
� � ? (Lesson 1-2)
A. 4 B. 0.4 C. 40 D. 0.04 1.
2. If 4 � 7 � 6 � 4 � 7 � 6 � n, what is the value of n? (Lesson 1-4)
E. 0 F. 1 G. 4 H. 6 2.
3. Lynn has 4 more books than José. If Lynn gives José 6 of her books, how many more will José have than Lynn? (Lesson 2-3)
A. 2 B. 4 C. 8 D. 10 3.
4. If x � �1264�
, which value of x does NOT form a proportion? (Lesson 2-6)
E. �23� F. �
34� G. �
1128�
H. �3428�
4.
5. Two-thirds of a number added to itself is 20. What is the number?(Lesson 3-1)
A. 12 B. 13 C. 30 D. 33 5.
6. 16% of 980 is 9.8% of what number? (Lesson 3-5)
E. 1.6 F. 16 G. 160 H. 1600 6.
7. For what value(s) of r is 3r � 6 � 7 � 3r? (Lesson 3-7)
A. all numbers B. all negative integersC. 0 D. no values of r 7.
8. The range of a relation includes the integers �4x
�, �5x
�, and �8x
�.
What could be a value for x in the domain? (Lesson 4-3)
E. 20 F. 30 G. 32 H. 40 8.
9. A line with a slope of �1 passes through points at (2, 3) and (5, y). Find the value of y. (Lesson 5-1)
A. �6 B. �3 C. 0 D. 6 9.
10. If a line passes through (0, �6) and has a slope of �3, what is an equation for the line? (Lesson 5-4)
E. y � �6x � 3 F. x � �6y � 3G. y � �3x � 6 H. x � �3y � 6 10. HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
NAME DATE PERIOD
55
Ass
essm
ent
Standardized Test Practice (Chapters 1–5)
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
© Glencoe/McGraw-Hill 342 Glencoe Algebra 1
Standardized Test Practice (continued)
11. If x2 � 16 and y2 � 4, what is the greatest 11. 12.possible value of (x � y)2? (Lesson 2-8)
12. If �x � 22x � 3x� � 6, x � ? (Lesson 3-4)
13. The formula for the volume of a rectangular 13. 14.solid is V � Bh. A packing crate has a height of 4.5 inches and a base area of 18.2 square inches. What is the volume of the crate in cubic inches? (Lesson 3-8)
14. Find the slope of a line parallel to 2y � x � 6.(Lesson 5-6)
Column A Column B
15.
On the number line above, the marks are equally spaced.
15.
(Lesson 2-1)
16. 3x � 5 � 20
16.
(Lesson 3-4)
DCBA406x
DCBA�1377�x
13
12
x
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
NAME DATE PERIOD
55
NAME DATE PERIOD NAME DATE PERIOD
A
D
C
B
Standardized Test PracticeStudent Record Sheet (Use with pages 314–315 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9
Solve the problem and write your answer in the blank.
For Questions 10, 12, and 14, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
10 (grid in) 10 12 14
11
12 (grid in)
13
14 (grid in)
15
16
17
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
55
An
swer
s
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Extended ResponsePart 3 Extended Response
Part 1 Multiple ChoicePart 1 Multiple Choice
Record your answers for Questions 18–19 on the back of this paper.
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
1G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Fin
d S
lop
e
Slo
pe
of
a L
ine
m�
or m
�,
whe
re (
x 1,
y 1)
and
(x2,
y2)
are
the
coo
rdin
ates
of a
ny t
wo
poin
ts o
n a
nonv
ertic
al li
ne
y 2�
y 1� x 2
�x 1
rise
� run
Fin
d t
he
slop
e of
th
eli
ne
that
pas
ses
thro
ugh
(�
3,5)
and
(4,
�2)
.
Let
(�
3,5)
�(x
1,y 1
) an
d (4
,�2)
�(x
2,y 2
).
m�
Slo
pe f
orm
ula
�y 2
��
2, y
1�
5, x
2�
4, x
1�
�3
�S
impl
ify.
��
1
�7
�7�
2 �
5�
�4
�(�
3)
y 2�
y 1� x
2�
x 1
Fin
d t
he
valu
e of
rso
th
at
the
lin
e th
rou
gh (
10,r
) an
d (
3,4)
has
a
slop
e of
�.
m�
Slo
pe f
orm
ula
��
m�
�,
y 2�
4, y
1�
r, x
2�
3, x
1�
10
��
Sim
plify
.
�2(
�7)
�7(
4 �
r)C
ross
mul
tiply
.
14 �
28 �
7rD
istr
ibut
ive
Pro
pert
y
�14
��
7rS
ubtr
act
28 f
rom
eac
h si
de.
2 �
rD
ivid
e ea
ch s
ide
by �
7.
4 �
r�
�7
2 � 7
2 � 7
4 �
r� 3
�10
2 � 7
y 2�
y 1� x
2�
x 1
2 � 7
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.(4
,9),
(1,6
)1
2.(�
4,�
1),(
�2,
�5)
�2
3.(�
4,�
1),(
�4,
�5)
un
def
ined
4.(2
,1),
(8,9
)5.
(14,
�8)
,(7,
�6)
�6.
(4,�
3),(
8,�
3)0
7.(1
,�2)
,(6,
2)8.
(2,5
),(6
,2)
�9.
(4,3
.5),
(�4,
3.5)
0
Det
erm
ine
the
valu
e of
rso
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts h
asth
e gi
ven
slo
pe.
10.(
6,8)
,(r,
�2)
,m�
1�
411
.(�
1,�
3),(
7,r)
,m�
312
.(2,
8),(
r,�
4) m
��
36
13.(
7,�
5),(
6,r)
,m�
0�
514
.(r,
4),(
7,1)
,m�
1115
.(7,
5),(
r,9)
,m�
6
16.(
10,r
),(3
,4),
m�
�17
.(10
,4),
(�2,
r),m
��
0.5
18.(
r,3)
,(7,
r),m
��
210
2
1 � 52 � 7
23 � 33 � 4
3 � 4
3 � 44 � 5
2 � 74 � 3
©G
lenc
oe/M
cGra
w-H
ill28
2G
lenc
oe A
lgeb
ra 1
Rat
e o
f C
han
ge
Th
e ra
teof
ch
ange
tell
s,on
ave
rage
,how
a q
uan
tity
is
chan
gin
g ov
erti
me.
Slo
pe d
escr
ibes
a r
ate
of c
han
ge.
POPU
LATI
ON
Th
e gr
aph
sh
ows
the
pop
ula
tion
gro
wth
in
Ch
ina.
a.F
ind
th
e ra
tes
of c
han
ge f
or 1
950–
1975
an
d f
or
1975
–200
0.
1950
–197
5:� �
or 0
.015
2
1975
–200
0:� �
or 0
.012
4
b.
Exp
lain
th
e m
ean
ing
of t
he
slop
e in
eac
h c
ase.
Fro
m 1
950–
1975
,th
e gr
owth
was
0.0
152
bill
ion
per
yea
r,or
15.
2 m
illi
on p
er y
ear.
Fro
m 1
975–
2000
,th
e gr
owth
was
0.0
124
bill
ion
per
yea
r,or
12.
4 m
illi
on p
er y
ear.
c.H
ow a
re t
he
dif
fere
nt
rate
s of
ch
ange
sh
own
on
th
e gr
aph
?T
her
e is
a g
reat
er v
erti
cal
chan
ge f
or 1
950–
1975
th
an f
or 1
975–
2000
.Th
eref
ore,
the
sect
ion
of
the
grap
h f
or 1
950–
1975
has
a s
teep
er s
lope
.
LON
GEV
ITY
Th
e gr
aph
sh
ows
the
pre
dic
ted
lif
e ex
pec
tan
cy f
or m
en a
nd
wom
en b
orn
in
a g
iven
yea
r.
1.F
ind
the
rate
s of
ch
ange
for
wom
en f
rom
200
0–20
25
and
2025
–205
0.0.
16/y
r,0.
12/y
r
2.F
ind
the
rate
s of
ch
ange
for
men
fro
m 2
000–
2025
an
d20
25–2
050.
0.16
/yr,
0.12
/yr
3.E
xpla
in t
he
mea
nin
g of
you
r re
sult
s in
Exe
rcis
es 1
an
d 2.
Bo
th m
en a
nd
wo
men
incr
ease
d t
hei
r lif
e ex
pec
tan
cy a
t th
e sa
me
rate
s.
4.W
hat
pat
tern
do
you
see
in
th
e in
crea
se w
ith
eac
h
25-y
ear
peri
od?
Wh
ile li
fe e
xpec
tan
cy
incr
ease
s,it
do
es n
ot
incr
ease
at
a co
nst
ant
rate
.
5.M
ake
a pr
edic
tion
for
th
e li
fe e
xpec
tan
cy f
or 2
050–
2075
.Exp
lain
how
you
arr
ived
at
you
r pr
edic
tion
.S
amp
le a
nsw
er:
89 f
or
wo
men
an
d 8
3 fo
r m
en;
the
dec
reas
e in
rat
e fr
om
200
0–20
25 t
o 2
025–
2050
is 0
.04/
yr.I
f th
e d
ecre
ase
in t
he
rate
rem
ain
s th
e sa
me,
the
chan
ge
of
rate
fo
r 20
50–2
075
mig
ht
be
0.08
/yr
and
25(
0.08
) �
2 ye
ars
of
incr
ease
ove
r th
e 25
-yea
r sp
an.
Pre
dic
tin
g L
ife E
xp
ect
an
cy
Year
Bo
rn
Age
2000
Wo
men
Men
100 95 90 85 80 75 70 65
2050
*20
25*
*Est
imat
ed
Sour
ce: U
SA T
OD
AY8084
8178
74
87
0.31
�251.24
�0.
93�
�20
00 �
1975
chan
ge i
n p
opu
lati
on�
��
chan
ge i
n t
ime
0.38
�250.
93 �
0.55
��
1975
�19
50ch
ange
in
pop
ula
tion
��
�ch
ange
in
tim
e
Po
pu
lati
on
Gro
wth
in
Ch
ina
Year
People (billions)
1950
1975
2000
2.0
1.5
1.0
0.5 0
2025
*
*Est
imat
ed
Sour
ce: U
nite
d Na
tions
Pop
ulat
ion
Divis
ion
0.55
0.93
1.24
1.48
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
Exer
cises
Exer
cises
Exam
ple
Exam
ple
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
3G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
2�
3
4.(2
,5),
(3,6
)1
5.(6
,1),
(�6,
1)0
6.(4
,6),
(4,8
)u
nd
efin
ed7.
(5,2
),(5
,�2)
un
def
ined
8.(2
,5),
(�3,
�5)
29.
(9,8
),(7
,�8)
8
10.(
�5,
�8)
,(�
8,1)
�3
11.(
�3,
10),
(�3,
7)u
nd
efin
ed
12.(
17,1
8),(
18,1
7)�
113
.(�
6,�
4),(
4,1)
14.(
10,0
),(�
2,4)
�15
.(2,
�1)
,(�
8,�
2)
16.(
5,�
9),(
3,�
2)�
17.(
12,6
),(3
,�5)
18.(
�4,
5),(
�8,
�5)
19.(
�5,
6),(
7,�
8)�
Fin
d t
he
valu
e of
rso
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts h
as t
he
give
n s
lop
e.
20.(
r,3)
,(5,
9),m
�2
221
.(5,
9),(
r,�
3),m
��
48
22.(
r,2)
,(6,
3),m
�4
23.(
r,4)
,(7,
1),m
�11
24.(
5,3)
,(r,
�5)
,m�
43
25.(
7,r)
,(4,
6),m
�0
6
3 � 41 � 2
7 � 65 � 2
11 � 97 � 2
1 � 101 � 3
1 � 2
1 � 3
( 0, 1
) ( 1, –
2)x
y
O
( 0, 0
)( 3, 1
)
x
y
O( 0
, 1)
( 2, 5
)
x
y O
©G
lenc
oe/M
cGra
w-H
ill28
4G
lenc
oe A
lgeb
ra 1
Fin
d t
he
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
�3
0
4.(6
,3),
(7,�
4)�
75.
(�9,
�3)
,(�
7,�
5)�
1
6.(6
,�2)
,(5,
�4)
27.
(7,�
4),(
4,8)
�4
8.(�
7,8)
,(�
7,5)
un
def
ined
9.(5
,9),
(3,9
)0
10.(
15,2
),(�
6,5)
�11
.(3,
9),(
�2,
8)
12.(
�2,
�5)
,(7,
8)13
.(12
,10)
,(12
,5)
un
def
ined
14.(
0.2,
�0.
9),(
0.5,
�0.
9)0
15. �
,�, �
�,
�
Fin
d t
he
valu
e of
rso
th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts h
as t
he
give
n s
lop
e.
16.(
�2,
r),(
6,7)
,m�
317
.(�
4,3)
,(r,
5),m
�4
18.(
�3,
�4)
,(�
5,r)
,m�
�5
19.(
�5,
r),(
1,3)
,m�
�4
20.(
1,4)
,(r,
5),m
un
defi
ned
121
.(�
7,2)
,(�
8,r)
,m�
�5
7
22.(
r,7)
,(11
,8),
m�
�16
23.(
r,2)
,(5,
r),m
�0
2
24.R
OO
FIN
GT
he
pitc
hof
a r
oof
is t
he
nu
mbe
r of
fee
t th
e ro
of r
ises
for
eac
h 1
2 fe
eth
oriz
onta
lly.
If a
roo
f h
as a
pit
ch o
f 8,
wh
at i
s it
s sl
ope
expr
esse
d as
a p
osit
ive
nu
mbe
r?
25. S
ALE
SA
dai
ly n
ewsp
aper
had
12,
125
subs
crib
ers
wh
en i
t be
gan
pu
blic
atio
n.F
ive
year
sla
ter
it h
ad 1
0,10
0 su
bscr
iber
s.W
hat
is
the
aver
age
year
ly r
ate
of c
han
ge i
n t
he
nu
mbe
rof
su
bscr
iber
s fo
r th
e fi
ve-y
ear
peri
od?
�40
5 su
bsc
rib
ers
per
yea
r
2 � 3
1 � 5
7 � 69 � 2
1 � 41 � 2
1 � 42 � 3
1 � 34 � 3
7 � 3
13 � 9
1 � 51 � 7
4 � 5
( –2,
3)
( 3, 3
)
x
y O
( 3, 1
)
( –2,
–3)
x
y
O( –
1, 0
)
( –2,
3)
x
y
OPra
ctic
e (
Ave
rag
e)
Slo
pe
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
lop
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
©G
lenc
oe/M
cGra
w-H
ill28
5G
lenc
oe A
lgeb
ra 1
Lesson 5-1
Pre-
Act
ivit
yW
hy
is s
lop
e im
por
tan
t in
arc
hit
ectu
re?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-1
at
the
top
of p
age
256
in y
our
text
book
.Th
en c
ompl
ete
the
defi
nit
ion
of
slop
e an
d fi
ll i
n t
he
boxe
son
th
e gr
aph
wit
h t
he
wor
ds r
ise
and
run
.
slop
e �
In t
his
gra
ph,t
he
rise
is
un
its,
and
the
run
is
un
its.
Th
us,
the
slop
e of
th
is l
ine
is
or
.
Rea
din
g t
he
Less
on
1.D
escr
ibe
each
typ
e of
slo
pe a
nd
incl
ude
a s
ketc
h.
Typ
e o
f S
lop
eD
escr
ipti
on
of
Gra
ph
Ske
tch
posi
tive
Th
e g
rap
h r
ises
as
you
go
fro
m le
ft t
o
rig
ht.
nega
tive
Th
e g
rap
h f
alls
as
you
go
fro
m le
ft t
o
rig
ht.
zero
Th
e g
rap
h is
a h
ori
zon
tal l
ine.
unde
fined
Th
e g
rap
h is
a v
erti
cal l
ine.
2.D
escr
ibe
how
eac
h e
xpre
ssio
n i
s re
late
d to
slo
pe.
a.d
iffe
ren
ce o
f y-
coo
rdin
ates
div
ided
by
dif
fere
nce
of
corr
esp
on
din
g x
-co
ord
inat
es
b.
ho
w f
ar u
p o
r d
ow
n a
s co
mp
ared
to
ho
w f
ar le
ft o
r ri
gh
t
c.sl
op
e u
sed
as
rate
of
chan
ge
Hel
pin
g Y
ou
Rem
emb
er3.
Th
e w
ord
rise
is u
sual
ly a
ssoc
iate
d w
ith
goi
ng
up.
Som
etim
es g
oin
g fr
om o
ne
poin
t on
the
grap
h d
oes
not
in
volv
e a
rise
an
d a
run
bu
t a
fall
an
d a
run
.Des
crib
e h
ow y
ou c
ould
sele
ct p
oin
ts s
o th
at i
t is
alw
ays
a ri
se f
rom
th
e fi
rst
poin
t to
th
e se
con
d po
int.
Sam
ple
an
swer
:If
th
e sl
op
e is
neg
ativ
e,ch
oo
se t
he
seco
nd
po
int
so t
hat
its
x-co
ord
inat
e is
less
th
an t
hat
of
the
firs
t p
oin
t.
$52,
000
incr
ease
in
spe
ndi
ng
��
��
26 m
onth
s
rise
� run
y 2�
y 1� x 2
�x 1
x
y
O
x
y
O
x
y
O
x
y
O
3 � 53
un
its
� 5u
nit
s
53
rise
� run
x
y
O
rise
run
©G
lenc
oe/M
cGra
w-H
ill28
6G
lenc
oe A
lgeb
ra 1
Trea
sure
Hu
nt
wit
h S
lop
esU
sin
g th
e d
efin
itio
n o
f sl
ope,
dra
w l
ines
wit
h t
he
slop
es l
iste
d
bel
ow.A
cor
rect
sol
uti
on w
ill
trac
e th
e ro
ute
to
the
trea
sure
.
1.3
2.3.
�4.
0
5.1
6.�
17.
no
slop
e8.
9.10
.11
.�
12.
33 � 4
1 � 33 � 2
2 � 7
2 � 51 � 4
Star
t Her
e
Trea
sure
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-1
5-1
Answers (Lesson 5-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Slo
pe
and
Dir
ect V
aria
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill28
7G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Dir
ect
Var
iati
on
A d
irec
t va
riat
ion
is d
escr
ibed
by
an e
quat
ion
of
the
form
y�
kx,
wh
ere
k�
0.W
e sa
y th
at y
var
ies
dir
ectl
y as
x.I
n t
he
equ
atio
n y
�kx
,kis
th
e co
nst
ant
of v
aria
tion
.
Nam
e th
e co
nst
ant
ofva
riat
ion
for
th
e eq
uat
ion
.Th
en f
ind
the
slop
e of
th
e li
ne
that
pas
ses
thro
ugh
th
e p
air
of p
oin
ts.
For
y�
x,th
e co
nst
ant
of v
aria
tion
is
.
m�
Slo
pe f
orm
ula
�(x
1, y
1) �
(0,
0),
(x2,
y2)
�(2
, 1)
�S
impl
ify.
Th
e sl
ope
is
.1 � 2
1 � 21 �
0� 2
�0
y 2�
y 1� x
2�
x 1
1 � 21 � 2
( 2, 1
)( 0
, 0)
x
y
Oy
� 1 2x
Su
pp
ose
yva
ries
dir
ectl
y as
x,a
nd
y�
30 w
hen
x�
5.
a.W
rite
a d
irec
t va
riat
ion
eq
uat
ion
that
rel
ates
xan
d y
.F
ind
the
valu
e of
k.
y�
kxD
irect
var
iatio
n eq
uatio
n
30 �
k(5)
Rep
lace
yw
ith 3
0 an
d x
with
5.
6 �
kD
ivid
e ea
ch s
ide
by 5
.
Th
eref
ore,
the
equ
atio
n i
s y
�6x
.
b.
Use
th
e d
irec
t va
riat
ion
eq
uat
ion
to
fin
d x
wh
en y
�18
.y
�6x
Dire
ct v
aria
tion
equa
tion
18 �
6xR
epla
ce y
with
18.
3 �
xD
ivid
e ea
ch s
ide
by 6
.
Th
eref
ore,
x�
3 w
hen
y�
18.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
qu
atio
n.T
hen
det
erm
ine
the
slop
e of
th
eli
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
�2;
�2
3;3
;
Wri
te a
dir
ect
vari
atio
n e
qu
atio
n t
hat
rel
ates
xto
y.A
ssu
me
that
yva
ries
dir
ectl
yas
x.T
hen
sol
ve.
4.If
y�
4 w
hen
x�
2,fi
nd
yw
hen
x�
16.
y�
2x;
325.
If y
�9
wh
en x
��
3,fi
nd
xw
hen
y�
6.y
��
3x;
�2
6.If
y�
�4.
8 w
hen
x�
�1.
6,fi
nd
x w
hen
y�
�24
.y
�3x
;�
87.
If y
�w
hen
x�
,fin
d x
wh
en y
�.
y�
2x;
3 � 323 � 16
1 � 81 � 4
3 � 23 � 2( –
2, –
3)
( 0, 0
)x
y O
y �
3 2x
( 1, 3
)
( 0, 0
)x
y
O
y �
3x
( –1,
2)
( 0, 0
)x
y
Oy
� –
2x
©G
lenc
oe/M
cGra
w-H
ill28
8G
lenc
oe A
lgeb
ra 1
Solv
e Pr
ob
lem
sT
he
dis
tan
ce f
orm
ula
d�
rtis
a d
irec
t va
riat
ion
equ
atio
n.I
n t
he
form
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,dis
tan
ce d
vari
es d
irec
tly
as t
ime
t,an
d th
e ra
te r
is t
he
con
stan
t of
var
iati
on.
TRA
VEL
A f
amil
y d
rove
th
eir
car
225
mil
es i
n 5
hou
rs.
a.W
rite
a d
irec
t va
riat
ion
eq
uat
ion
to
fin
d t
he
dis
tan
ce t
rave
led
for
an
y n
um
ber
of h
ours
.U
se g
iven
val
ues
for
dan
d t
to f
ind
r.d
�rt
Orig
inal
equ
atio
n
225
�r(
5)d
�22
5 an
d t�
5
45�
rD
ivid
e ea
ch s
ide
by 5
.
Th
eref
ore,
the
dire
ct v
aria
tion
equ
atio
n i
s d
�45
t.b
.G
rap
h t
he
equ
atio
n.
Th
e gr
aph
of
d�
45t
pass
es t
hro
ugh
th
e or
igin
wit
hsl
ope
45.
m�
✓C
HEC
K(5
,225
) li
es o
n t
he
grap
h.
c.E
stim
ate
how
man
y h
ours
it
wou
ld t
ake
the
fam
ily
to d
rive
360
mil
es.
d�
45t
Orig
inal
equ
atio
n
360
�45
tR
epla
ce d
with
360
.
t�
8D
ivid
e ea
ch s
ide
by 4
5.
Th
eref
ore,
it w
ill
take
8 h
ours
to
driv
e 36
0 m
iles
.
RET
AIL
Th
e to
tal
cost
Cof
bu
lk j
elly
bea
ns
is
$4.4
9 ti
mes
th
e n
um
ber
of
pou
nd
s p
.
1.W
rite
a d
irec
t va
riat
ion
equ
atio
n t
hat
rel
ates
th
e va
riab
les.
C�
4.49
p2.
Gra
ph t
he
equ
atio
n o
n t
he
grid
at
the
righ
t.
3.F
ind
the
cost
of
pou
nd
of je
lly
bean
s.$3
.37
CH
EMIS
TRY
Ch
arle
s’s
Law
sta
tes
that
,at
a co
nst
ant
pre
ssu
re,v
olu
me
of a
gas
Vva
ries
dir
ectl
y as
its
tem
per
atu
reT
.A v
olu
me
of 4
cu
bic
fee
t of
a c
erta
in g
as h
as a
tem
per
atu
reof
200
°(a
bso
lute
tem
per
atu
re).
V�
0.02
T4.
Wri
te a
dir
ect
vari
atio
n e
quat
ion
th
at r
elat
es t
he
vari
able
s.
5.G
raph
th
e eq
uat
ion
on
th
e gr
id a
t th
e ri
ght.
5 ft
3
6.F
ind
the
volu
me
of t
he
sam
e ga
s at
250
°(a
bsol
ute
tem
pera
ture
).
Ch
arl
es’
s La
w
Tem
per
atu
re (
�K)
Volume (cubic feet)
100
020
0T
V 4 3 2 1
3 � 4
Co
st o
f Je
lly B
ean
s
Wei
gh
t (p
ou
nd
s)
Cost (dollars)
20
4w
C
18.0
0
13.5
0
9.00
4.50
rise
� run
45 � 1
Au
tom
ob
ile T
rip
s
Tim
e (h
ou
rs)
Distance (miles)
10
23
45
67
8t
d
360
270
180 90
( 1, 4
5)
( 5, 2
25)
d �
45t
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Slo
pe
and
Dir
ect V
aria
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Slo
pe
and
Dir
ect V
aria
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill28
9G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
qu
atio
n.T
hen
det
erm
ine
the
slop
e of
th
eli
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.;
2.�
2;�
23.
�;
�
Gra
ph
eac
h e
qu
atio
n.
4.y
�3x
5.y
��
x6.
y�
x
Wri
te a
dir
ect
vari
atio
n e
qu
atio
n t
hat
rel
ates
xan
d y
.Ass
um
e th
at y
vari
esd
irec
tly
as x
.Th
en s
olve
.
7.If
y�
�8
wh
en x
��
2,fi
nd
x8.
If y
�45
wh
en x
�15
,fin
d x
wh
en y
�32
.y
�4x
;8
wh
en y
�15
.y
�3x
;5
9.If
y�
�4
wh
en x
�2,
fin
d y
10.I
f y
��
9 w
hen
x�
3,fi
nd
yw
hen
x�
�6.
y�
�2x
;12
wh
en x
��
5.y
��
3x;
15
11.I
f y
�4
wh
en x
�16
,fin
d y
12.I
f y
�12
wh
en x
�18
,fin
d x
wh
en x
�6.
y�
x;w
hen
y�
�16
.y
�x;
�24
Wri
te a
dir
ect
vari
atio
n e
qu
atio
n t
hat
rel
ates
th
e va
riab
les.
Th
en g
rap
h t
he
equ
atio
n.
13. T
RA
VEL
Th
e to
tal
cost
Cof
gas
olin
e
14.S
HIP
PIN
GT
he
nu
mbe
r of
del
iver
ed t
oys
Tis
$1.
80 t
imes
th
e n
um
ber
of g
allo
ns
g.is
3 t
imes
th
e to
tal
nu
mbe
r of
cra
tes
c.
C�
1.80
gT
�3c
Toys
Sh
ipp
ed
Cra
tes
Toys
20
46
71
35
c
T
21 18 15 12 9 6 3
Gaso
lin
e C
ost
Gal
lon
s
Cost ($)
40
812
142
610
g
C 28 24 20 16 12 8 4
2 � 33 � 2
1 � 4
x
y
O
2 � 5
x
y
O
3 � 4
x
y
O
3 � 23 � 2( –
2, 3
)
( 0, 0
)x
y
O
y �
– 3 2x
( –1,
2)
( 0, 0
)x
y
O
y �
–2x
1 � 31 � 3
( 3, 1
)( 0
, 0)
x
y O
y �
1 3x
©G
lenc
oe/M
cGra
w-H
ill29
0G
lenc
oe A
lgeb
ra 1
Nam
e th
e co
nst
ant
of v
aria
tion
for
eac
h e
qu
atio
n.T
hen
det
erm
ine
the
slop
e of
th
eli
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.;
2.;
3.�
;�
Gra
ph
eac
h e
qu
atio
n.
4.y
��
2x5.
y�
x6.
y�
�x
Wri
te a
dir
ect
vari
atio
n e
qu
atio
n t
hat
rel
ates
xan
d y
.Ass
um
e th
at y
vari
esd
irec
tly
as x
.Th
en s
olve
.
7.If
y�
7.5
wh
en x
�0.
5,fi
nd
yw
hen
x�
�0.
3.y
�15
x;�
4.5
8.If
y�
80 w
hen
x�
32,f
ind
xw
hen
y�
100.
y�
2.5x
;40
9.If
y�
wh
en x
�24
,fin
d y
wh
en x
�12
.y
�x;
Wri
te a
dir
ect
vari
atio
n e
qu
atio
n t
hat
rel
ates
th
e va
riab
les.
Th
en g
rap
h t
he
equ
atio
n.
10. M
EASU
RE
Th
e w
idth
Wof
a
11.T
ICK
ETS
Th
e to
tal
cost
Cof
tic
kets
is
rect
angl
e is
tw
o th
irds
of
the
len
gth
�.
$4.5
0 ti
mes
th
e n
um
ber
of t
icke
ts t
.
W�
�C
�4.
50t
12.P
RO
DU
CE
Th
e co
st o
f ba
nan
as v
arie
s di
rect
ly w
ith
th
eir
wei
ght.
Mig
uel
bou
ght
3po
un
ds o
f ba
nan
as f
or $
1.12
.Wri
te a
n e
quat
ion
th
at r
elat
es t
he
cost
of
the
ban
anas
to t
hei
r w
eigh
t.T
hen
fin
d th
e co
st o
f 4
pou
nds
of
ban
anas
.C
�0.
32p
;$1
.36
1 � 4
1 � 2
Co
st o
f Ti
ckets
Tick
ets
Cost ($)
20
46
13
5t
C 25 20 15 10 5
Rect
an
gle
Dim
en
sio
ns
Len
gth
Width
40
812
26
10�
W 10 8 6 4 2
2 � 3
3 � 81 � 32
3 � 4
x
y
O
5 � 3
x
y
O
6 � 5
x
y
O
5 � 25 � 2
( –2,
5)
( 0, 0
)x
y
O
y �
� 5 2x
4 � 34 � 3
( 3, 4
)
( 0, 0
)x
y O
y �
4 3x
3 � 43 � 4
( 4, 3
)
( 0, 0
)x
y O
y �
3 4x
Pra
ctic
e (
Ave
rag
e)
Slo
pe
and
Dir
ect V
aria
tio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csS
lop
e an
d D
irec
t Var
iati
on
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
©G
lenc
oe/M
cGra
w-H
ill29
1G
lenc
oe A
lgeb
ra 1
Lesson 5-2
Pre-
Act
ivit
yH
ow i
s sl
ope
rela
ted
to
you
r sh
ower
?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-2
at
the
top
of p
age
264
in y
our
text
book
.
•H
ow d
o th
e n
um
bers
in
th
e ta
ble
rela
te t
o th
e gr
aph
sh
own
?T
hey
are
th
e co
ord
inat
es o
f th
e p
oin
ts o
n t
he
gra
ph
.
•T
hin
k ab
out
the
firs
t se
nte
nce
.Wh
at d
oes
it m
ean
to
say
that
a s
tan
dard
show
erh
ead
use
s ab
out
6 ga
llon
s of
wat
er p
er m
inu
te?
Sam
ple
an
swer
:F
or
each
min
ute
th
e sh
ow
er r
un
s,6
gal
lon
so
f w
ater
co
me
ou
t.S
o,i
f th
e sh
ow
er r
an 1
0 m
inu
tes,
that
wo
uld
be
60 g
allo
ns.
Rea
din
g t
he
Less
on
1.W
hat
is
the
form
of
a di
rect
var
iati
on e
quat
ion
?y
�kx
2.H
ow i
s th
e co
nst
ant
of v
aria
tion
rel
ated
to
slop
e?T
he
con
stan
t o
f va
riat
ion
has
the
sam
e va
lue
as t
he
slo
pe
of
the
gra
ph
of
the
equ
atio
n.
3.T
he
expr
essi
on “
yva
ries
dir
ectl
y as
x”
can
be
wri
tten
as
the
equ
atio
n y
�kx
.How
wou
ldyo
u w
rite
an
equ
atio
n f
or “
wva
ries
dir
ectl
y as
th
e sq
uar
e of
t”?
w�
kt2
4.F
or e
ach
sit
uat
ion
,wri
te a
n e
quat
ion
wit
h t
he
prop
er c
onst
ant
of v
aria
tion
.
a.T
he
dist
ance
dva
ries
dir
ectl
y as
tim
e t,
and
a ch
eeta
h c
an t
rave
l 88
fee
t in
1 s
econ
d.d
�88
t
b.
Th
e pe
rim
eter
pof
a p
enta
gon
wit
h a
ll s
ides
of
equ
al l
engt
h v
arie
s di
rect
ly a
s th
ele
ngt
h s
of a
sid
e of
th
e pe
nta
gon
.A p
enta
gon
has
5 s
ides
.p
�5s
c.T
he
wag
es W
earn
ed b
y an
em
ploy
ee v
ary
dire
ctly
wit
h t
he
nu
mbe
r of
hou
rs h
that
are
wor
ked.
En
riqu
e ea
rned
$17
2.50
for
23
hou
rs o
f w
ork.
W�
$7.5
0h
Hel
pin
g Y
ou
Rem
emb
er
5.L
ook
up
the
wor
d co
nst
ant
in a
dic
tion
ary.
How
doe
s th
is d
efin
itio
n r
elat
e to
th
e te
rmco
nst
ant
of v
aria
tion
?S
amp
le a
nsw
er:
So
met
hin
g u
nch
ang
ing
;th
e co
nst
ant
of
vari
atio
n r
elat
es x
and
yin
th
e sa
me
valu
e ev
ery
tim
e,an
d t
hat
rela
tio
nsh
ip n
ever
ch
ang
es.
©G
lenc
oe/M
cGra
w-H
ill29
2G
lenc
oe A
lgeb
ra 1
nth
Po
wer
Var
iati
on
An
equa
tion
of
the
form
y�
kxn ,
whe
re k
�0,
desc
ribe
s an
nth
pow
erva
riat
ion.
The
var
iabl
e n
can
be r
epla
ced
by 2
to
indi
cate
the
sec
ond
pow
erof
x(t
he s
quar
e of
x)
or b
y 3
to in
dica
te t
he t
hird
pow
er o
f x
(the
cub
e of
x).
Ass
um
e th
at t
he
wei
ght
of a
per
son
of
aver
age
buil
d va
ries
dir
ectl
y as
th
ecu
be o
f th
at p
erso
n’s
hei
ght.
Th
e eq
uat
ion
of
vari
atio
n h
as t
he
form
w
�kh
3 .
The
wei
ght
that
a p
erso
n’s
legs
wil
l sup
port
is p
ropo
rtio
nal t
o th
e cr
oss-
sect
iona
l are
a of
the
leg
bone
s.T
his
area
var
ies
dire
ctly
as
the
squa
reof
the
per
son’
s he
ight
.The
equ
atio
n of
var
iati
on h
as t
he f
orm
s�
kh2 .
An
swer
eac
h q
ues
tion
.
1.F
or a
per
son
6 f
eet
tall
wh
o w
eigh
s 20
0 po
un
ds,f
ind
a va
lue
for
kin
th
e eq
uat
ion
w�
kh3 .
k�
0.93
2.U
se y
our
answ
er f
rom
Exe
rcis
e 1
to p
redi
ct t
he
wei
ght
of a
per
son
wh
o is
5 f
eet
tall
.ab
ou
t 11
6 p
ou
nd
s
3.F
ind
the
valu
e fo
r k
in t
he
equ
atio
n w
�kh
3fo
r a
baby
wh
o is
20
inch
es
lon
g an
d w
eigh
s 6
pou
nds
.
k�
1.29
6 fo
r h
�ft
4.H
ow d
oes
you
r an
swer
to
Exe
rcis
e 3
dem
onst
rate
th
at a
bab
y is
si
gnif
ican
tly
fatt
er i
n p
ropo
rtio
n t
o it
s h
eigh
t th
an a
n a
dult
?
kh
as a
gre
ater
val
ue.
5.F
or a
per
son
6 f
eet
tall
wh
o w
eigh
s 20
0 po
un
ds,f
ind
a va
lue
for
kin
th
e eq
uat
ion
s�
kh2 .
k�
5.56
6.F
or a
bab
y w
ho
is 2
0 in
ches
lon
g an
d w
eigh
s 6
pou
nds
,fin
d an
“in
fan
t va
lue”
for
kin
th
e eq
uat
ion
s�
kh2 .
k�
2.16
fo
r h
�ft
7.A
ccor
din
g to
th
e ad
ult
equ
atio
n y
ou f
oun
d (E
xerc
ise
1),h
ow m
uch
w
ould
an
im
agin
ary
gian
t 20
fee
t ta
ll w
eigh
?
7440
po
un
ds
8.A
ccor
din
g to
th
e ad
ult
equ
atio
n f
or w
eigh
t su
ppor
ted
(Exe
rcis
e 5)
,how
m
uch
wei
ght
cou
ld a
20-
foot
tal
l gi
ant’s
leg
s ac
tual
ly s
upp
ort?
on
ly 2
224
po
un
ds
9.W
hat
can
you
con
clu
de f
rom
Exe
rcis
es 7
an
d 8?
An
swer
s w
ill v
ary.
Fo
r ex
amp
le,b
on
e st
ren
gth
lim
its
the
size
hu
man
sca
n a
ttai
n.
5 � 3
5 � 3
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-2
5-2
Answers (Lesson 5-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Slo
pe-
Inte
rcep
t F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
3G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Slo
pe-
Inte
rcep
t Fo
rm
Slo
pe-
Inte
rcep
t F
orm
y�
mx
�b,
whe
re m
is t
he g
iven
slo
pe a
nd b
is t
he y
-inte
rcep
t
Wri
te a
n e
qu
atio
n o
f th
e li
ne
wh
ose
slop
e is
�4
and
wh
ose
y-in
terc
ept
is 3
.y
�m
x�
bS
lope
-inte
rcep
t fo
rm
y�
�4x
�3
Rep
lace
mw
ith �
4 an
d b
with
3.
Gra
ph
3x
�4y
�8.
3x�
4y�
8O
rigin
al e
quat
ion
�4y
��
3x�
8S
ubtr
act
3xfr
om e
ach
side
.
�D
ivid
e ea
ch s
ide
by �
4.
y�
x�
2S
impl
ify.
Th
e y-
inte
rcep
t of
y�
x�
2 is
�2
and
the
slop
e is
.S
o gr
aph
th
e po
int
(0,�
2).F
rom
this
poi
nt,
mov
e u
p 3
un
its
and
righ
t 4
un
its.
Dra
w a
lin
e pa
ssin
g th
rou
gh b
oth
poi
nts
.
Wri
te a
n e
qu
atio
n o
f th
e li
ne
wit
h t
he
give
n s
lop
e an
d y
-in
terc
ept.
1.sl
ope:
8,y-
inte
rcep
t �
32.
slop
e:�
2,y-
inte
rcep
t �
13.
slop
e:�
1,y-
inte
rcep
t �
7y
�8x
�3
y�
�2x
�1
y�
�x
�7
Wri
te a
n e
qu
atio
n o
f th
e li
ne
show
n i
n e
ach
gra
ph
.
4.5.
6.
y�
2x�
2y
��
x�
3y
�x
�5
Gra
ph
eac
h e
qu
atio
n.
7.y
�2x
�1
8.y
��
3x�
29.
y�
�x
�1
x
y
Ox
y
Ox
y
O
3 � 4
( 4, –
2)
( 0, –
5)
xy
O
( 3, 0
)
( 0, 3
)
x
y
O( 0
, –2)
( 1, 0
)x
y
O
3 � 43 � 4
3 � 4�3x
�8
��
�4
�4y
� �4
( 0, –
2)
( 4, 1
)
x
y
O
3x �
4y
� 8
Exam
ple
1Ex
ampl
e 1
Exam
ple
2Ex
ampl
e 2
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill29
4G
lenc
oe A
lgeb
ra 1
Mo
del
Rea
l-W
orl
d D
ata
MED
IAS
ince
199
7,th
e n
um
ber
of
cab
le T
V s
yste
ms
has
dec
reas
edb
y an
ave
rage
rat
e of
121
sys
tem
s p
er y
ear.
Th
ere
wer
e 10
,943
sys
tem
s in
199
7.
a.W
rite
a l
inea
r eq
uat
ion
to
fin
d t
he
aver
age
nu
mb
er o
f ca
ble
sys
tem
s in
an
y ye
araf
ter
1997
.T
he
rate
of
chan
ge i
s �
121
syst
ems
per
year
.In
th
e fi
rst
year
,th
e n
um
ber
of s
yste
ms
was
10,9
43.L
et N
�th
e nu
mbe
r of
cab
le T
V s
yste
ms.
Let
x�
the
num
ber
of y
ears
aft
er 1
997.
An
equa
tion
isN
��
121x
�10
,943
.
b.
Gra
ph
th
e eq
uat
ion
.T
he
grap
h o
f N
��
121x
�10
,943
is
a li
ne
that
pas
ses
thro
ugh
th
e po
int
at (
0,10
,943
) an
d h
as a
slo
pe o
f �
121.
c.F
ind
th
e ap
pro
xim
ate
nu
mb
er o
f ca
ble
TV
sy
stem
s in
200
0.N
��
121x
�10
,943
Orig
inal
equ
atio
n
N�
�12
1(3)
�10
,943
Rep
lace
xw
ith 3
.
N�
10,5
80S
impl
ify.
Th
ere
wer
e ab
out
10,5
80 c
able
TV
sys
tem
s in
200
0.
ENTE
RTA
INM
ENT
In 1
995,
65.7
% o
f al
l h
ouse
hol
ds
wit
h T
V’s
in
th
e U
.S.s
ub
scri
bed
to
cab
le T
V.B
etw
een
199
5an
d 1
999,
the
per
cen
t in
crea
sed
by
abou
t 0.
6% e
ach
yea
r.
1.W
rite
an
equ
atio
n t
o fi
nd
the
perc
ent
Pof
hou
seh
olds
th
atsu
bscr
ibed
to
cabl
e T
V f
or a
ny
year
xbe
twee
n 1
995
and
1999
.P
�0.
6x�
65.7
2.G
raph
th
e eq
uat
ion
on
th
e gr
id a
t th
e ri
ght.
3.F
ind
the
perc
ent
that
su
bscr
ibed
to
cabl
e T
V i
n 1
999.
68.1
%
POPU
LATI
ON
Th
e p
opu
lati
on o
f th
e U
nit
ed S
tate
s is
p
roje
cted
to
be
300
mil
lion
by
the
year
201
0.B
etw
een
20
10 a
nd
205
0,th
e p
opu
lati
on i
s ex
pec
ted
to
incr
ease
by
abou
t 2.
5 m
illi
on p
er y
ear.
4.W
rite
an
equ
atio
n t
o fi
nd
the
popu
lati
on P
in a
ny
year
xbe
twee
n 2
010
and
2050
.P
�2,
500,
000x
�30
0,00
0,00
0
5.G
raph
th
e eq
uat
ion
on
th
e gr
id a
t th
e ri
ght.
6.F
ind
the
popu
lati
on i
n 2
050.
abo
ut
400,
000,
000
Pro
ject
ed
Un
ited
Sta
tes
Po
pu
lati
on
Year
s Si
nce
201
0
Population (millions)
020
40x
P
400
380
360
340
320
300
Sour
ce: T
he W
orld
Alm
anac
Perc
en
t o
f H
ou
seh
old
sw
ith
TV
Havin
g C
ab
le
Year
s Si
nce
199
5
Percent
10
23
45
x
P
68 67 66 65
Sour
ce: T
he W
orld
Alm
anac
Cab
le T
V S
yst
em
s
Year
s Si
nce
199
7
Number of Cable TV Systems
10
23
45
6x
N
10,9
00
10,8
00
10,7
00
10,6
00
10,5
00
Sour
ce: T
he W
orld
Alm
anac
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Slo
pe-
Inte
rcep
t F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Slo
pe-
Inte
rcep
t F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
5G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Wri
te a
n e
qu
atio
n o
f th
e li
ne
wit
h t
he
give
n s
lop
e an
d y
-in
terc
ept.
1.sl
ope:
5,y-
inte
rcep
t:�
3y
�5x
�3
2.sl
ope:
�2,
y-in
terc
ept:
7y
��
2x�
7
3.sl
ope:
�6,
y-in
terc
ept:
�2
y�
�6x
�2
4.sl
ope:
7,y-
inte
rcep
t:1
y�
7x�
1
5.sl
ope:
3,y-
inte
rcep
t:2
y�
3x�
26.
slop
e:�
4,y-
inte
rcep
t:�
9y
��
4x�
9
7.sl
ope:
1,y-
inte
rcep
t:�
12y
�x
�12
8.sl
ope:
0,y-
inte
rcep
t:8
y�
8
Wri
te a
n e
qu
atio
n o
f th
e li
ne
show
n i
n e
ach
gra
ph
.
9.10
.11
.
y�
2x�
3y
��
3x�
2y
��
x�
1
Gra
ph
eac
h e
qu
atio
n.
12.y
�x
�4
13.y
��
2x�
114
.x�
y�
�3
Wri
te a
lin
ear
equ
atio
n i
n s
lop
e-in
terc
ept
form
to
mod
el e
ach
sit
uat
ion
.
15.A
vid
eo s
tore
ch
arge
s $1
0 fo
r a
ren
tal
card
plu
s $2
per
ren
tal.
C�
2r�
10
16.A
Nor
folk
pin
e is
18
inch
es t
all
and
grow
s at
a r
ate
of 1
.5 f
eet
per
year
.H
�1.
5t�
1.5
17.A
Cai
rn t
erri
er w
eigh
s 30
pou
nds
an
d is
on
a s
peci
al d
iet
to l
ose
2 po
un
ds p
er m
onth
.W
��
2m�
30
18.A
n a
irpl
ane
at a
n a
ltit
ude
of
3000
fee
t de
scen
ds a
t a
rate
of
500
feet
per
mil
e.A
��
500m
�30
00
x
y
O
x
y
Ox
y
O
( 0, –
1)( 2
, –3)
x
y O
( 0, 2
)
( 2, –
4)
x
y
O( 2
, 1)
( 0, –
3)
x
y
O
©G
lenc
oe/M
cGra
w-H
ill29
6G
lenc
oe A
lgeb
ra 1
Wri
te a
n e
qu
atio
n o
f th
e li
ne
wit
h t
he
give
n s
lop
e an
d y
-in
terc
ept.
1.sl
ope:
,y-i
nte
rcep
t:3
y�
x�
32.
slop
e:,y
-in
terc
ept:
�4
y�
x�
4
3.sl
ope:
1.5,
y-in
terc
ept:
�1
4.sl
ope:
�2.
5,y-
inte
rcep
t:3.
5y
�1.
5x�
1y
��
2.5x
�3.
5
Wri
te a
n e
qu
atio
n o
f th
e li
ne
show
n i
n e
ach
gra
ph
.
5.6.
7.
y�
x�
2y
�x
�3
y�
�x
�2
Gra
ph
eac
h e
qu
atio
n.
8.y
��
x�
29.
3y�
2x�
610
.6x
�3y
�6
Wri
te a
lin
ear
equ
atio
n i
n s
lop
e-in
terc
ept
form
to
mod
el e
ach
sit
uat
ion
.
11.A
com
pute
r te
chni
cian
cha
rges
$75
for
a c
onsu
ltat
ion
plus
$35
per
hou
r.C
�35
h�
75
12.T
he
popu
lati
on o
f P
ine
Blu
ff i
s 67
91 a
nd
is d
ecre
asin
g at
th
e ra
te o
f 7
per
year
.P
��
7t�
6791
WR
ITIN
GF
or E
xerc
ises
13–
15,u
se t
he
foll
owin
g in
form
atio
n.
Car
la h
as a
lrea
dy w
ritt
en 1
0 pa
ges
of a
nov
el.S
he
plan
sto
wri
te 1
5 ad
diti
onal
pag
es p
er m
onth
un
til
she
is f
inis
hed
.
13.W
rite
an
equ
atio
n t
o fi
nd
the
tota
l n
um
ber
of p
ages
Pw
ritt
en a
fter
an
y n
um
ber
of m
onth
s m
.P
�10
�15
m
14.G
raph
th
e eq
uat
ion
on
th
e gr
id a
t th
e ri
ght.
15.F
ind
the
tota
l n
um
ber
of p
ages
wri
tten
aft
er 5
mon
ths.
85
Carl
a’s
No
vel
Mo
nth
s
Pages Written
20
46
13
5m
P
100 80 60 40 20
x
y
Ox
y
Ox
y
O1 � 2
2 � 33 � 2
2 � 5
( –3,
0)
( 0, –
2)
x
y
O( –
2, 0
)
( 0, 3
)
x
y O( –
5, 0
)
( 0, 2
)
x
y
O
3 � 23 � 2
1 � 41 � 4P
ract
ice (
Ave
rag
e)
Slo
pe-
Inte
rcep
t F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
lop
e-In
terc
ept
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
©G
lenc
oe/M
cGra
w-H
ill29
7G
lenc
oe A
lgeb
ra 1
Lesson 5-3
Pre-
Act
ivit
yH
ow i
s a
y-in
terc
ept
rela
ted
to
a fl
at f
ee?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-3
at
the
top
of p
age
272
in y
our
text
book
.
•W
hat
poi
nt
on t
he
grap
h s
how
s th
at t
he
flat
fee
is
$5.0
0?(0
,5)
•H
ow d
oes
the
rate
of
$0.1
0 pe
r m
inu
te r
elat
e to
th
e gr
aph
?It
is t
he
slo
pe.
Rea
din
g t
he
Less
on
1.F
ill
in t
he
boxe
s w
ith
th
e co
rrec
t w
ords
to
desc
ribe
wh
at m
and
bre
pres
ent.
y�
mx
�b
↑↑
2.W
hat
are
th
e sl
ope
and
y-in
terc
ept
of a
ver
tica
l li
ne?
Th
e sl
op
e is
un
def
ined
,an
d t
her
e is
no
y-i
nte
rcep
t.
3.W
hat
are
th
e sl
ope
and
y-in
terc
ept
of a
hor
izon
tal
lin
e?
Th
e sl
op
e is
0,a
nd
th
e y-
inte
rcep
t is
wh
ere
it c
ross
es t
he
y-ax
is.
4.R
ead
the
prob
lem
.Th
en a
nsw
er e
ach
par
t of
th
e ex
erci
se.
A r
uby
-th
roat
ed h
um
min
gbir
d w
eigh
s ab
out
0.6
gram
at
birt
h a
nd
gain
s w
eigh
t at
a r
ate
of a
bou
t 0.
2 gr
am p
er d
ay u
nti
l fu
lly
grow
n.
a.W
rite
a v
erba
l eq
uat
ion
to
show
how
th
e w
ords
are
rel
ated
to
fin
din
g th
e av
erag
ew
eigh
t of
a r
uby
-th
roat
ed h
um
min
gbir
d at
an
y gi
ven
wee
k.U
se t
he
wor
ds w
eigh
t at
birt
h,r
ate
of g
row
th,w
eigh
t,an
d w
eeks
aft
er b
irth
.Bel
ow t
he
equ
atio
n,f
ill
in a
ny
valu
es y
ou k
now
an
d pu
t a
ques
tion
mar
k u
nde
r th
e it
ems
that
you
do
not
kn
ow.
��
�
b.
Def
ine
wh
at v
aria
bles
to
use
for
th
e u
nkn
own
qu
anti
ties
.S
amp
le a
nsw
er:
Let
W
be
the
wei
gh
t at
any
tim
e an
d t
be
the
nu
mb
er o
f w
eeks
aft
er b
irth
.
c.U
se t
he
vari
able
s yo
u d
efin
ed a
nd
wh
at y
ou k
now
fro
m t
he
prob
lem
to
wri
te a
neq
uat
ion
.W
�0.
2t�
0.6
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to a
not
her
per
son
.Wri
te h
ow y
ou w
ould
expl
ain
to
som
eon
e th
e pr
oces
s fo
r u
sin
g th
e y-
inte
rcep
t an
d sl
ope
to g
raph
a l
inea
req
uat
ion
.O
n t
he
y-ax
is,p
lot
the
po
int
for
the
y-in
terc
ept.
Th
en u
se t
he
rise
-ove
r-ru
n d
efin
itio
n o
f sl
op
e to
det
erm
ine
ho
w f
ar u
p o
r d
ow
n a
nd
rig
ht
or
left
th
e n
ext
po
int
is f
rom
th
e fi
rst.
y-in
terc
ept
slo
pe
wei
gh
t?
rate
of
gro
wth
0.2
wee
ks a
fter
bir
th?
wei
gh
t at
bir
th0.
6
©G
lenc
oe/M
cGra
w-H
ill29
8G
lenc
oe A
lgeb
ra 1
Rel
atin
g S
lop
e-In
terc
ept
Fo
rm a
nd
Sta
nd
ard
Fo
rms
You
hav
e le
arn
ed t
hat
slo
pe c
an b
e de
fin
ed i
n t
erm
s of
or
.
An
oth
er d
efin
itio
n c
an b
e fo
un
d fr
om t
he
stan
dard
fro
m o
f a
lin
ear
equ
atio
n.S
tan
dard
for
m i
s A
x�
By
�C
,wh
ere
A,B
,an
d C
are
inte
gers
,A�
0,an
d A
and
Bar
e n
ot b
oth
zer
o.
1.S
olve
Ax
�B
y�
C f
or y
.You
r an
swer
sh
ould
be
wri
tten
in
sl
ope-
inte
rcep
t fo
rm.
y�
�x
�
2.U
se t
he
slop
e-in
terc
ept
equ
atio
n y
ou w
rote
in
Exe
rcis
e 1
to w
rite
ex
pres
sion
s fo
r th
e sl
ope
and
the
y-in
terc
ept
in t
erm
s of
A,B
,an
d C
.
m�
�,b
�
Use
th
e ex
pre
ssio
ns
in E
xerc
ise
2 ab
ove
to f
ind
th
e sl
ope
and
y-
inte
rcep
t of
eac
h e
qu
atio
n.
3.2x
�y
��
44.
4x�
3y�
24
m�
�2,
b�
�4
m�
�,b
�8
5.4x
�6y
��
366.
x�
3y�
�27
m�
�,b
��
6m
�,b
�9
7.x
�2y
�6
8.4y
�20
m�
,b�
�3
m�
0,b
�5
1 � 2
1 � 32 � 3
4 � 3
C � BA � B
C � BA � B
y 2�
y 1� x 2
�x 1
rise
� run
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-3
5-3
Answers (Lesson 5-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g E
qu
atio
ns
in S
lop
e-In
terc
ept
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill29
9G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Wri
te a
n E
qu
atio
n G
iven
th
e Sl
op
e an
d O
ne
Poin
t
Wri
te a
n e
qu
atio
n o
fa
lin
e th
at p
asse
s th
rou
gh (
�4,
2)w
ith
slo
pe
3.
Th
e li
ne
has
slo
pe 3
.To
fin
d th
e y-
inte
rcep
t,re
plac
e m
wit
h 3
an
d (x
,y)
wit
h (
�4,
2) i
n t
he
slop
e-in
terc
ept
form
.T
hen
sol
ve f
or b
.y
�m
x�
bS
lope
-inte
rcep
t fo
rm
2 �
3(�
4) �
bm
�3,
y�
2, a
nd x
��
4
2 �
�12
�b
Mul
tiply
.
14 �
bA
dd 1
2 to
eac
h si
de.
Th
eref
ore,
the
equ
atio
n i
s y
�3x
�14
.
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
(�
2,�
1) w
ith
slo
pe
.
Th
e li
ne
has
slo
pe
.Rep
lace
mw
ith
an
d (x
,y)
wit
h (
�2,
�1)
in
th
e sl
ope-
inte
rcep
t fo
rm.
y�
mx
�b
Slo
pe-in
terc
ept
form
�1
�(�
2) �
bm
�,
y�
�1,
and
x�
�2
�1
��
�b
Mul
tiply
.
��
bA
dd
to e
ach
side
.
Th
eref
ore,
the
equ
atio
n i
s y
�x
�.
1 � 21 � 4
1 � 2
1 � 2
1 � 2
1 � 4
1 � 4
1 � 41 � 4
1 � 4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
oin
t w
ith
th
e gi
ven
slo
pe.
1.2.
3.
y�
2x�
1y
��
2xy
�x
�3
4.(8
,2),
m�
�5.
(�1,
�3)
,m�
56.
(4,�
5),m
��
y�
�x
�8
y�
5x�
2y
��
x�
3
7.(�
5,4)
,m�
08.
(2,2
),m
�9.
(1,�
4),m
��
6
y�
4y
�x
�1
y�
�6x
�2
10.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh t
he
y-in
terc
ept
�3
wit
h s
lope
2.
y�
2x�
3
11.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh t
he
x-in
terc
ept
4 w
ith
slo
pe �
3.y
��
3x�
12
12.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh t
he
poin
t (0
,350
) w
ith
slo
pe
.
y�
x�
350
1 � 5
1 � 5
1 � 2
1 � 2
1 � 23 � 4
1 � 23 � 4
1 � 2
( 2, 4
)
x
y
O
m �
1 2
( 0, 0
)x
y
O
m �
–2
( 3, 5
)
x
y
O
m �
2
©G
lenc
oe/M
cGra
w-H
ill30
0G
lenc
oe A
lgeb
ra 1
Wri
te a
n E
qu
atio
n G
iven
Tw
o P
oin
ts
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
(1,
2) a
nd
(3,
�2)
.
Fin
d th
e sl
ope
m.T
o fi
nd
the
y-in
terc
ept,
repl
ace
mw
ith
its
com
pute
d va
lue
and
(x,y
) w
ith
(1,2
) in
th
e sl
ope-
inte
rcep
t fo
rm.T
hen
sol
ve f
or b
.
m�
Slo
pe f
orm
ula
m�
y 2�
�2,
y1
�2,
x2
�3,
x1
�1
m�
�2
Sim
plify
.
y�
mx
�b
Slo
pe-in
terc
ept
form
2 �
�2(
1) �
bR
epla
ce m
with
�2,
yw
ith 2
, an
d x
with
1.
2 �
�2
�b
Mul
tiply
.
4 �
bA
dd 2
to
each
sid
e.
Th
eref
ore,
the
equ
atio
n i
s y
��
2x�
4.
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
1.2.
3.
y�
4x�
3y
��
x�
4y
�x
�1
4.(�
1,6)
,(7,
�10
)5.
(0,2
),(1
,7)
6.(6
,�25
),(�
1,3)
y�
�2x
�4
y�
5x�
2y
��
4x�
1
7.(�
2,�
1),(
2,11
)8.
(10,
�1)
,(4,
2)9.
(�14
,�2)
,(7,
7)
y�
3x�
5y
��
x�
4y
�x
�4
10.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh t
he
x-in
terc
ept
4 an
d y-
inte
rcep
t �
2.
y�
x�
2
11.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh t
he
x-in
terc
ept
�3
and
y-in
terc
ept
5.
y�
x�
5
12.W
rite
an
equ
atio
n o
f a
lin
e th
at p
asse
s th
rou
gh (
0,16
) an
d (�
10,0
).
y�
x�
168 � 55 � 31 � 2
3 � 71 � 2
1 � 3( 0, 1
)
( –3,
0)
x
y
O
( 0, 4
) ( 4, 0
)x
y
O
( 1, 1
)
( 0, –
3)
x
y
O
�2
�2
�3
�1
y 2�
y 1� x
2�
x 1Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Wri
tin
g E
qu
atio
ns
in S
lop
e-In
terc
ept
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Wri
tin
g E
qu
atio
ns
in S
lop
e-In
terc
ept
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill30
1G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
oin
t w
ith
th
e gi
ven
slo
pe.
1.2.
3.
y�
�3x
�1
y�
x�
3y
�2x
�4
4.(1
,9),
m�
45.
(4,2
),m
��
26.
(2,�
2),m
�3
y�
4x�
5y
��
2x�
10y
�3x
�8
7.(3
,0),
m�
58.
(�3,
�2)
,m�
29.
(�5,
4),m
��
4y
�5x
�15
y�
2x�
4y
��
4x�
16
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
10.
11.
12.
y�
�x
�1
y�
2x�
1y
��
2x�
3
13.(
1,3)
,(�
3,�
5)14
.(1,
4),(
6,�
1)15
.(1,
�1)
,(3,
5)y
�2x
�1
y�
�x
�5
y�
3x�
4
16.(
�2,
4),(
0,6)
17.(
3,3)
,(1,
�3)
18.(
�1,
6),(
3,�
2)y
�x
�6
y�
3x�
6y
��
2x�
4
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
has
eac
h p
air
of i
nte
rcep
ts.
19.x
-in
terc
ept:
�3,
y-in
terc
ept:
620
.x-i
nte
rcep
t:3,
y-in
terc
ept:
3
y�
2x�
6y
��
x�
3
21.x
-in
terc
ept:
1,y-
inte
rcep
t:2
22.x
-in
terc
ept:
2,y-
inte
rcep
t:�
4
y�
�2x
�2
y�
2x�
4
23.x
-in
terc
ept:
�4,
y-in
terc
ept:
�8
24.x
-in
terc
ept:
�1,
y-in
terc
ept:
4
y�
�2x
�8
y�
4x�
4
( 2, –
1)
( 0, 3
)
x
y
O( –
1, –
3)
( 1, 1
)x
y
O
( –2,
3)
( 3, –
2)
x
y
O
( –1,
2)
x
y O
m �
2
( 4, 1
)
x
y
O
m �
1
( –1,
4)
x
y
O
m �
–3
©G
lenc
oe/M
cGra
w-H
ill30
2G
lenc
oe A
lgeb
ra 1
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
oin
t w
ith
th
e gi
ven
slo
pe.
1.2.
3.
y�
3x�
1y
��
2x�
2y
��
x�
4
4.(�
5,4)
,m�
�3
5.(4
,3),
m�
6.(1
,�5)
,m�
�
y�
�3x
�11
y�
x�
1y
��
x�
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
eac
h p
air
of p
oin
ts.
7.8.
9.
y�
x�
6y
��
x�
5y
��
2x�
5
10.(
0,�
4),(
5,�
4)11
.(�
4,�
2),(
4,0)
12.(
�2,
�3)
,(4,
5)
y�
�4
y�
x�
1y
�x
�
13.(
0,1)
,(5,
3)14
.(�
3,0)
,(1,
�6)
15.(
1,0)
,(5,
�1)
y�
x�
1y
��
x�
y�
�x
�
Wri
te a
n e
qu
atio
n o
f th
e li
ne
that
has
eac
h p
air
of i
nte
rcep
ts.
16.x
-in
terc
ept:
2,y-
inte
rcep
t:�
517
.x-i
nte
rcep
t:2,
y-in
terc
ept:
10
y�
x�
5y
��
5x�
10
18.x
-in
terc
ept:
�2,
y-in
terc
ept:
119
.x-i
nte
rcep
t:�
4,y-
inte
rcep
t:�
3
y�
x�
1y
��
x�
3
20.D
AN
CE
LESS
ON
ST
he
cost
for
7 d
ance
les
son
s is
$82
.Th
e co
st f
or 1
1 le
sson
s is
$12
2.W
rite
a l
inea
r eq
uat
ion
to
fin
d th
e to
tal
cost
Cfo
r �
less
ons.
Th
en u
se t
he
equ
atio
n t
ofi
nd
the
cost
of
4 le
sson
s.C
�10
��
12;
$52
21.W
EATH
ERIt
is
76°F
at
the
6000
-foo
t le
vel
of a
mou
nta
in,a
nd
49°F
at
the
12,0
00-f
oot
leve
l of
th
e m
oun
tain
.Wri
te a
lin
ear
equ
atio
n t
o fi
nd
the
tem
pera
ture
Tat
an
ele
vati
one
on t
he
mou
nta
in,w
her
e e
is i
n t
hou
san
ds o
f fe
et.
T�
�4.
5e�
103
3 � 41 � 25 � 2
1 � 41 � 4
9 � 23 � 2
2 � 5
1 � 34 � 3
1 � 4
( –3,
1)
( –1,
–3)
x
y
O( 0
, 5)
( 4, 1
) x
y
O
( 4, –
2)
( 2, –
4)
xy
O
7 � 23 � 2
1 � 2
3 � 21 � 2
( –1,
–3)
x
y
O
m �
–1
( –2,
2)
x
y O
m �
–2
( 1, 2
)
x
y
Om
� 3
Pra
ctic
e (
Ave
rag
e)
Wri
tin
g E
qu
atio
ns
in S
lop
e-In
terc
ept
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csW
riti
ng
Eq
uat
ion
s in
Slo
pe-
Inte
rcep
t F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
©G
lenc
oe/M
cGra
w-H
ill30
3G
lenc
oe A
lgeb
ra 1
Lesson 5-4
Pre-
Act
ivit
yH
ow c
an s
lop
e-in
terc
ept
form
be
use
d t
o m
ake
pre
dic
tion
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-4
at
the
top
of p
age
280
in y
our
text
book
.
•W
hat
is
the
rate
of
chan
ge p
er y
ear?
abo
ut
2000
per
yea
r•
Stu
dy t
he
patt
ern
on
th
e gr
aph
.How
wou
ld y
ou f
ind
the
popu
lati
on i
n19
97?
Ad
d 2
000
to t
he
1996
po
pu
lati
on
,wh
ich
giv
es 1
79,0
00.
Rea
din
g t
he
Less
on
1.S
upp
ose
you
are
giv
en t
hat
a l
ine
goes
th
rou
gh (
2,5)
an
d h
as a
slo
pe o
f �
2.U
se t
his
info
rmat
ion
to
com
plet
e th
e fo
llow
ing
equ
atio
n.
y�
mx
�b
↓↓
��
�
2.W
hat
mu
st y
ou f
irst
do
if y
ou a
re n
ot g
iven
th
e sl
ope
in t
he
prob
lem
?
Use
th
e in
form
atio
n g
iven
(tw
o p
oin
ts)
to f
ind
th
e sl
op
e.
3.W
hat
is
the
firs
t st
ep i
n a
nsw
erin
g an
y st
anda
rdiz
ed t
est
prac
tice
qu
esti
on?
Rea
d t
he
pro
ble
m.
4.W
hat
are
fou
r st
eps
you
can
use
in
sol
vin
g a
wor
d pr
oble
m?
Exp
lore
,Pla
n,S
olv
e,E
xam
ine
5.D
efin
e th
e te
rm l
inea
r ex
trap
olat
ion
.
Lin
ear
extr
apo
lati
on
mea
ns
usi
ng
a li
nea
r eq
uat
ion
to
pre
dic
t va
lues
th
atar
e o
uts
ide
the
two
giv
en d
ata
po
ints
.
Hel
pin
g Y
ou
Rem
emb
er
6.In
you
r ow
n w
ords
,exp
lain
how
you
wou
ld a
nsw
er a
qu
esti
on t
hat
ask
s yo
u t
o w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n.
Sam
ple
an
swer
:D
eter
min
e w
hat
info
rmat
ion
yo
u a
re g
iven
.If
you
hav
e a
po
int
and
th
e sl
op
e,yo
u c
ansu
bst
itu
te t
he
x- a
nd
y-v
alu
es a
nd
th
e sl
op
e in
to y
�m
x�
bto
fin
d t
he
valu
e o
f b
.Th
en u
se t
he
valu
es o
f m
and
bto
wri
te t
he
equ
atio
n.I
f yo
uh
ave
two
po
ints
,use
th
em t
o f
ind
th
e sl
op
e,an
d t
hen
use
th
e m
eth
od
fo
ra
po
int
and
th
e sl
op
e.
b2
�2
5
©G
lenc
oe/M
cGra
w-H
ill30
4G
lenc
oe A
lgeb
ra 1
Cel
siu
s an
d K
elvi
n T
emp
erat
ure
sIf
you
blo
w u
p a
ball
oon
an
d pu
t it
in
th
e re
frig
erat
or,t
he
ball
oon
wil
l sh
rin
k as
th
e te
mpe
ratu
re o
f th
e ai
r in
th
e ba
lloo
n d
ecre
ases
.
Th
e vo
lum
e of
a c
erta
in g
as i
s m
easu
red
at 3
0°C
elsi
us.
Th
e te
mpe
ratu
re i
s de
crea
sed
and
the
volu
me
is m
easu
red
agai
n.
1.G
raph
th
is t
able
on
th
e co
ordi
nat
e pl
ane
prov
ided
bel
ow.
2.F
ind
the
equ
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
e po
ints
you
gr
aph
ed i
n E
xerc
ise
1.
v�
t�
182
3.U
se t
he
equ
atio
n y
ou f
oun
d in
Exe
rcis
e 2
to f
ind
the
tem
pera
ture
th
at w
ould
giv
e a
volu
me
of z
ero.
Th
is t
empe
ratu
re i
s th
e lo
wes
t on
e po
ssib
le a
nd
is c
alle
d ab
solu
te z
ero.
�27
3�C
4.In
184
8,L
ord
Kel
vin
pro
pose
d a
new
tem
pera
ture
sca
le w
ith
0
bein
g as
sign
ed t
o ab
solu
te z
ero.
Th
e si
ze o
f th
e de
gree
ch
osen
was
th
e sa
me
size
as
the
Cel
siu
s de
gree
.Ch
ange
eac
h o
f th
e C
elsi
us
tem
pera
ture
s in
th
e ta
ble
abov
e to
deg
rees
Kel
vin
.
303�
,294
�,27
3�,2
61�,
246�
2 � 3
t (�C
)
V(m
L)
O
200
100
10�
10�
20�
3020
30
Tem
per
atu
re (
t)Vo
lum
e (V
)
30°C
202
mL
21°C
196
mL
0°C
182
mL
–12°
C17
4 m
L–2
7°C
164
mL
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-4
5-4
Answers (Lesson 5-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Wri
tin
g E
qu
atio
ns
in P
oin
t-S
lop
e F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
5G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Poin
t-Sl
op
e Fo
rm
Po
int-
Slo
pe
Fo
rmy
�y 1
�m
(x�
x 1),
whe
re (
x 1,
y 1)
is a
giv
en p
oint
on
a no
nver
tical
line
an
d m
is t
he s
lope
of
the
line
Wri
te t
he
poi
nt-
slop
e fo
rmof
an
eq
uat
ion
for
a l
ine
that
pas
ses
thro
ugh
(6,
1) a
nd
has
a s
lop
e of
�.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
1 �
�(x
�6)
m�
�;
(x1,
y1)
�(6
, 1)
Th
eref
ore,
the
equ
atio
n i
s y
�1�
�(x
�6)
.5 � 2
5 � 25 � 2
5 � 2
Wri
te t
he
poi
nt-
slop
efo
rm o
f an
eq
uat
ion
for
a h
oriz
onta
lli
ne
that
pas
ses
thro
ugh
(4,
�1)
.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
(�1)
�0(
x�
4)m
�0;
(x 1
, y 1
) �
(4,
�1)
y�
1 �
0S
impl
ify.
Th
eref
ore,
the
equ
atio
n i
s y
�1
�0.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
eq
uat
ion
for
a l
ine
that
pas
ses
thro
ugh
eac
hp
oin
t w
ith
th
e gi
ven
slo
pe.
1.2.
3.
y�
1�x
�4
y�
2 �
0y
�3
��
2(x
�2)
4.(2
,1),
m�
45.
(�7,
2),m
�6
6.(8
,3),
m�
1
y�
1 �
4(x
�2)
y�
2 �
6(x
�7)
y�
3�x
� 8
7.(�
6,7)
,m�
08.
(4,9
),m
�9.
(�4,
�5)
,m�
�
y�
7 �
0y
�9
�(x
�4)
y�
5��
(x�
4)
10.W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n f
or t
he
hor
izon
tal
lin
e th
at p
asse
s th
rou
gh (
4,�
2).
y�
2 �
0
11.W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n f
or t
he
hor
izon
tal
lin
e th
at p
asse
s th
rou
gh (
�5,
6).
y�
6 �
0
12.W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n f
or t
he
hor
izon
tal
lin
e th
at p
asse
s th
rou
gh (
5,0)
.y
�0
1 � 23 � 4
1 � 23 � 4
( 2, –
3)
x
y
O
m �
–2
( –3,
2)
x
y
O
m �
0( 4
, 1)
x
y
O
m �
1
©G
lenc
oe/M
cGra
w-H
ill30
6G
lenc
oe A
lgeb
ra 1
Form
s o
f Li
nea
r Eq
uat
ion
s
Slo
pe-
Inte
rcep
t F
orm
y�
mx
�b
m�
slop
e; b
�y-
inte
rcep
t
Po
int-
Slo
pe
Fo
rmy
�y 1
�m
(x�
x 1)
m�
slop
e; (
x 1,
y 1)
is a
giv
en p
oint
.
Sta
nd
ard
A
x�
By
�C
Aan
d B
are
not
both
zer
o. U
sual
ly A
is n
onne
gativ
e an
d A
, B
, an
d C
Fo
rmar
e in
tege
rs w
hose
gre
ates
t co
mm
on f
acto
r is
1.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Wri
tin
g E
qu
atio
ns
in P
oin
t-S
lop
e F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
Wri
te y
�5
�(x
�6)
in
stan
dar
d f
orm
.
y�
5 �
(x�
6)O
rigin
al e
quat
ion
3(y
�5)
�3 �
�(x�
6)M
ultip
ly e
ach
side
by
3.
3y�
15 �
2(x
�6)
Dis
trib
utiv
e P
rope
rty
3y�
15 �
2x�
12D
istr
ibut
ive
Pro
pert
y
3y�
2x�
27S
ubtr
act
15 f
rom
eac
h si
de.
�2x
�3y
��
27A
dd �
2xto
eac
h si
de.
2x�
3y�
27M
ultip
ly e
ach
side
by
�1.
Th
eref
ore,
the
stan
dard
for
m o
f th
e eq
uat
ion
is 2
x�
3y�
27.2 � 3
2 � 3
2 � 3W
rite
y�
2 �
�(x
�8)
in s
lop
e-in
terc
ept
form
.
y�
2 �
�(x
�8)
Orig
inal
equ
atio
n
y�
2 �
�x
�2
Dis
trib
utiv
e P
rope
rty
y�
�x
�4
Add
2 t
o ea
ch s
ide.
Th
eref
ore,
the
slop
e-in
terc
ept
form
of
the
equ
atio
n i
s y
��
x�
4.1 � 4
1 � 41 � 41 � 4
1 � 4Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m.
1.y
�2
��
3(x
�1)
2.y
�1
��
(x�
6)3.
y�
2 �
(x�
9)
3x�
y�
1x
�3y
�9
2x�
3y�
24
4.y
�3
��
(x�
5)5.
y�
4 �
(x�
3)6.
y�
4 �
�(x
�1)
x�
y�
25x
�3y
��
272x
�5y
��
18
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
7.y
�4
�4(
x�
2)8.
y�
5 �
(x�
6)9.
y�
8 �
�(x
�8)
y�
4x�
12y
�x
�3
y�
�x
�6
10.y
�6
�3 �x
��
11.y
�4
��
2(x
�5)
12.y
��
(x�
2)
y�
3x�
5y
��
2x�
14y
�x
�8 � 3
1 � 2
1 � 25 � 3
1 � 3
1 � 41 � 3
1 � 41 � 3
2 � 55 � 3
2 � 31 � 3
Exer
cises
Exer
cises
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Wri
tin
g E
qu
atio
ns
in P
oin
t-S
lop
e F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
7G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
eq
uat
ion
for
a l
ine
that
pas
ses
thro
ugh
eac
hp
oin
t w
ith
th
e gi
ven
slo
pe.
1.2.
3.
y�
2 �
3(x
�1)
y�
2 �
�(x
�1)
y�
3 �
0
4.(3
,1),
m�
05.
(�4,
6),m
�8
6.(1
,�3)
,m�
�4
y�
1 �
0y
�6
�8(
x�
4)y
�3
��
4(x
�1)
7.(4
,�6)
,m�
18.
(3,3
),m
�9.
(�5,
�1)
,m�
�
y�
6 �
x�
4y
�3
�(x
�3)
y�
1 �
�(x
�5)
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m.
10.y
�1
�x
�2
11.y
�9
��
3(x
�2)
12.y
�7
�4(
x�
4)
x�
y�
�1
3x�
y�
�3
4x�
y�
�23
13.y
�4
��
(x�
1)14
.y�
6 �
4(x
�3)
15.y
�5
��
5(x
�3)
x�
y�
54x
�y
��
185x
�y
�10
16.y
�10
��
2(x
�3)
17.y
�2
��
(x�
4)18
.y�
11 �
(x�
3)
2x�
y�
16x
�2y
�8
x�
3y�
30
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
19.y
�4
�3(
x�
2)20
.y�
2 �
�(x
�4)
21.y
�6
��
2(x
�2)
y�
3x�
2y
��
x�
6y
��
2x�
2
22.y
�1
��
5(x
�3)
23.y
�3
�6(
x�
1)24
.y�
8 �
3(x
�5)
y�
�5x
�14
y�
6x�
3y
�3x
�23
25.y
�2
�(x
�6)
26.y
�1
��
(x�
9)27
.y�
�x
�
y�
x�
5y
��
x�
4y
�x
�1
1 � 31 � 2
1 � 21 � 2
1 � 31 � 2
1 � 31 � 2
5 � 44 � 3
5 � 44 � 3
( 2, –
3)
x
y O
m �
0
( 1, –
2)x
y O
m �
–1
( –1,
–2)
x
y
O
m �
3
©G
lenc
oe/M
cGra
w-H
ill30
8G
lenc
oe A
lgeb
ra 1
Wri
te t
he
poi
nt-
slop
e fo
rm o
f an
eq
uat
ion
for
a l
ine
that
pas
ses
thro
ugh
eac
hp
oin
t w
ith
th
e gi
ven
slo
pe.
1.(2
,2),
m�
�3
2.(1
,�6)
,m�
�1
3.(�
3,�
4),m
�0
y�
2 �
�3(
x�
2)y
�6
��
(x�
1)y
�4
�0
4.(1
,3),
m�
�5.
(�8,
5),m
��
6.(3
,�3)
,m�
y�
3 �
�(x
�1)
y�
5 �
�(x
�8)
y�
3 �
(x�
3)
Wri
te e
ach
eq
uat
ion
in
sta
nd
ard
for
m.
7.y
�11
�3(
x�
2)8.
y�
10 �
�(x
�2)
9.y
�7
�2(
x�
5)3x
�y
��
5x
�y
�12
2x�
y�
�3
10.y
�5
�(x
�4)
11.y
�2
��
(x�
1)12
.y�
6 �
(x�
3)
3x�
2y�
�22
3x�
4y�
�11
4x�
3y�
�6
13.y
�4
�1.
5(x
�2)
14.y
�3
��
2.4(
x�
5)15
.y�
4 �
2.5(
x�
3)3x
�2y
�2
12x
�5y
�75
5x�
2y�
�23
Wri
te e
ach
eq
uat
ion
in
slo
pe-
inte
rcep
t fo
rm.
16.y
�2
�4(
x�
2)17
.y�
1 �
�7(
x�
1)18
.y�
3 �
�5(
x�
12)
y�
4x�
6y
��
7x�
8y
��
5x�
57
19.y
�5
�(x
�4)
20.y
��
�3 �x
��
21.y
��
�2 �x
��
y�
x�
11y
��
3x�
y�
�2x
�
CO
NST
RU
CTI
ON
For
Exe
rcis
es 2
2–24
,use
th
e fo
llow
ing
info
rmat
ion
.A
con
stru
ctio
n c
ompa
ny
char
ges
$15
per
hou
r fo
r de
bris
rem
oval
,plu
s a
one-
tim
e fe
e fo
r th
eu
se o
f a
tras
h d
um
pste
r.T
he
tota
l fe
e fo
r 9
hou
rs o
f se
rvic
e is
$19
5.
22.W
rite
the
poi
nt-s
lope
for
m o
f an
equ
atio
n to
fin
d th
e to
tal f
ee y
for
any
num
ber
of h
ours
x.
y�
195
�15
(x�
9)
23.W
rite
th
e eq
uat
ion
in
slo
pe-i
nte
rcep
t fo
rm.
y�
15x
�60
24.W
hat
is
the
fee
for
the
use
of
a tr
ash
du
mps
ter?
$60
MO
VIN
GF
or E
xerc
ises
25–
27,u
se t
he
foll
owin
g in
form
atio
n.
The
re is
a s
et d
aily
fee
for
ren
ting
a m
ovin
g tr
uck,
plus
a c
harg
e of
$0.
50 p
er m
ile
driv
en.
It c
osts
$64
to
rent
the
tru
ck o
n a
day
whe
n it
is d
rive
n 48
mil
es.
25.W
rite
th
e po
int-
slop
e fo
rm o
f an
equ
atio
n t
o fi
nd
the
tota
l ch
arge
yfo
r an
y n
um
ber
ofm
iles
xfo
r a
one-
day
ren
tal.
y�
64 �
0.5
(x�
48)
26.W
rite
th
e eq
uat
ion
in
slo
pe-i
nte
rcep
t fo
rm.
y�
0.5x
�40
27.W
hat
is
the
dail
y fe
e?$4
0
7 � 61 � 2
3 � 2
1 � 42 � 3
1 � 41 � 4
3 � 2
4 � 33 � 4
3 � 2
1 � 32 � 5
3 � 4
1 � 32 � 5
3 � 4
Pra
ctic
e (
Ave
rag
e)
Wri
tin
g E
qu
atio
ns
in P
oin
t-S
lop
e F
orm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csW
riti
ng
Eq
uat
ion
s in
Po
int-
Slo
pe
Fo
rm
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
©G
lenc
oe/M
cGra
w-H
ill30
9G
lenc
oe A
lgeb
ra 1
Lesson 5-5
Pre-
Act
ivit
yH
ow c
an y
ou u
se t
he
slop
e fo
rmu
la t
o w
rite
an
eq
uat
ion
of
a li
ne?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-5
at
the
top
of p
age
286
in y
our
text
book
.
Not
e th
at i
n t
he
fin
al e
quat
ion
th
ere
is a
val
ue
subt
ract
ed f
rom
xan
d fr
om y
.Wh
at a
re t
hes
e va
lues
?T
he
valu
e su
btr
acte
d f
rom
xis
th
e x-
coo
rdin
ate
of
the
giv
enp
oin
t.T
he
valu
e su
btr
acte
d f
rom
yis
th
e y-
coo
rdin
ate
of
the
giv
en p
oin
t.
Rea
din
g t
he
Less
on
1.In
th
e fo
rmu
la y
�y 1
�m
(x�
x 1),
wh
at d
o x 1
and
y 1re
pres
ent?
x 1an
d y
1re
pre
sen
t th
e co
ord
inat
es o
f an
y g
iven
po
int
on
th
e g
rap
h
of
the
line.
2.C
ompl
ete
the
char
t be
low
by
list
ing
thre
e fo
rms
of e
quat
ion
s.T
hen
wri
te t
he
form
ula
for
each
for
m.F
inal
ly,w
rite
th
ree
exam
ples
of
equ
atio
ns
in t
hos
e fo
rms.
Sam
ple
exa
mp
les
are
giv
en.
Fo
rm o
f E
qu
atio
nF
orm
ula
Exa
mp
le
slo
pe-
inte
rcep
ty
�m
x�
by
�3x
�2
po
int-
slo
pe
y�
y 1�
m(x
�x 1
)y
�2
�4
(x�
3)
stan
dar
dA
x�
By
�C
3x�
5y�
15
3.R
efer
to
Exa
mpl
e 5
on p
age
288
of y
our
text
book
.Wh
at d
o yo
u t
hin
k th
e h
ypot
enu
seof
ari
ght
tria
ngl
e is
?S
amp
le a
nsw
ers:
Th
e hy
po
ten
use
is t
he
lon
ges
t si
de
of
the
rig
ht
tria
ng
le.T
he
hyp
ote
nu
se is
th
e si
de
op
po
site
th
e ri
gh
t an
gle
ina
rig
ht
tria
ng
le.
Hel
pin
g Y
ou
Rem
emb
er
4.S
upp
ose
you
cou
ld n
ot r
emem
ber
all
thre
e fo
rmu
las
list
ed i
n t
he
tabl
e ab
ove.
Wh
ich
of
the
form
s w
ould
you
con
cen
trat
e on
for
wri
tin
g li
nea
r eq
uat
ion
s? E
xpla
in w
hy
you
ch
ose
that
for
m.
Sam
ple
an
swer
:P
oin
t-sl
op
e fo
rm;
the
slo
pe-
inte
rcep
t fo
rm
can
be
wri
tten
fro
m t
he
po
int-
slo
pe
form
.Th
is is
so
bec
ause
th
e y-
inte
rcep
t le
ts y
ou
wri
te t
he
coo
rdin
ates
of
the
po
int
wh
ere
the
line
cro
sses
th
e y-
axis
.Yo
u c
an u
se t
hat
po
int
as t
he
giv
en p
oin
t in
th
e p
oin
t-sl
op
e fo
rmu
la.
©G
lenc
oe/M
cGra
w-H
ill31
0G
lenc
oe A
lgeb
ra 1
Co
llin
eari
ty
You
hav
e le
arn
ed h
ow t
o fi
nd
the
slop
e be
twee
n t
wo
poin
ts o
n a
lin
e.D
oes
it m
atte
r w
hic
h t
wo
poin
ts y
ou u
se?
How
doe
s yo
ur
choi
ce o
f po
ints
aff
ect
the
slop
e-in
terc
ept
form
of
the
equ
atio
n o
f th
e li
ne?
1.C
hoo
se t
hre
e di
ffer
ent
pair
s of
poi
nts
fro
m t
he
grap
h a
t th
e ri
ght.
Wri
te t
he
slop
e-in
terc
ept
form
of
the
lin
e u
sin
g ea
ch p
air.
y�
1x�
1
2.H
ow a
re t
he
equ
atio
ns
rela
ted?
Th
ey a
re t
he
sam
e.
3.W
hat
con
clu
sion
can
you
dra
w f
rom
you
r an
swer
s to
Exe
rcis
es 1
an
d 2?
Th
e eq
uat
ion
of
a lin
e is
th
e sa
me
no
mat
ter
wh
ich
tw
o p
oin
ts
you
ch
oo
se.
Wh
en p
oin
ts a
re c
onta
ined
in
th
e sa
me
lin
e,th
ey a
re s
aid
to b
e co
llin
ear.
Eve
n th
ough
poi
nts
may
loo
kli
ke t
hey
form
a s
trai
ght
line
whe
n co
nnec
ted,
it d
oes
not
mea
n t
hat
th
ey a
ctu
ally
do.
By
chec
kin
g pa
irs
of p
oin
ts o
n a
li
ne
you
can
det
erm
ine
wh
eth
er t
he
lin
e re
pres
ents
a l
inea
r re
lati
onsh
ip.
4.C
hoo
se s
ever
al p
airs
of
poin
ts f
rom
th
e gr
aph
at
the
righ
t an
d w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f th
e li
ne
usi
ng
each
pai
r.
y�
1x�
0;y
�2x
�2;
y�
2x�
1
5.W
hat
con
clu
sion
can
you
dra
w f
rom
you
r eq
uat
ion
s in
E
xerc
ise
4? I
s th
is a
str
aigh
t li
ne?
Th
e p
oin
ts a
re n
ot
colli
nea
r.T
his
is n
ot
a st
raig
ht
line.
x
y O
x
y
O
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-5
5-5
Answers (Lesson 5-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Geo
met
ry:P
aral
lel a
nd
Per
pen
dic
ula
r L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
1G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Para
llel L
ines
Tw
o n
onve
rtic
alli
nes
are
par
alle
lif
th
ey h
ave
the
sam
e sl
ope.
All
ve
rtic
al l
ines
are
par
alle
l.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
eq
uat
ion
of
the
lin
e th
atp
asse
s th
rou
gh (
�1,
6) a
nd
is
par
alle
l to
th
e gr
aph
of
y�
2x�
12.
A l
ine
para
llel
to
y�
2x�
12 h
as t
he
sam
e sl
ope,
2.R
epla
ce m
wit
h 2
an
d (x
1,y 1
) w
ith
(�
1,6)
in
th
e po
int-
slop
e fo
rm.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
6 �
2(x
�(�
1))
m�
2; (
x 1,
y 1)
�(�
1, 6
)
y�
6 �
2(x
�1)
Sim
plify
.
y�
6 �
2x�
2D
istr
ibut
ive
Pro
pert
y
y�
2x�
8S
lope
-inte
rcep
t fo
rm
Th
eref
ore,
the
equ
atio
n i
s y
�2x
�8.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
aral
lel
to t
he
grap
h o
f ea
ch e
qu
atio
n.
1.2.
3.
y�
x�
4y
��
x�
3y
�x
�7
4.(�
2,2)
,y�
4x�
25.
(6,4
),y
�x
�1
6.(4
,�2)
,y�
�2x
�3
y�
4x�
10y
�x
�2
y�
�2x
�6
7.(�
2,4)
,y�
�3x
�10
8.(�
1,6)
,3x
�y
�12
9.(4
,�6)
,x�
2y�
5
y�
�3x
�2
y�
�3x
�3
y�
�x
�4
10.F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
2 t
hat
is
para
llel
to
the
grap
h o
fth
e li
ne
4x�
2y�
8.y
��
2x�
2
11.F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
�1
that
is
para
llel
to
the
grap
h o
fth
e li
ne
x�
3y�
6.y
�x
�1
12.F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
�4
that
is
para
llel
to
the
grap
h o
fth
e li
ne
y�
6.y
��
4
1 � 3
1 � 2
1 � 3
1 � 3
4 � 31 � 2
( –3,
3)
x
y
O
4x �
3y
� –
12
( –8,
7)
x
y
O
y �
–1 2x
� 4
2
2
( 5, 1
)x
y
O
y �
x �
8
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill31
2G
lenc
oe A
lgeb
ra 1
Perp
end
icu
lar
Lin
esT
wo
lin
es a
re p
erp
end
icu
lar
if t
hei
r sl
opes
are
neg
ativ
ere
cipr
ocal
s of
eac
h o
ther
.Ver
tica
l an
d h
oriz
onta
l li
nes
are
per
pen
dicu
lar.
Wri
te t
he
slop
e-in
terc
ept
form
for
an
eq
uat
ion
th
at p
asse
s th
rou
gh(�
4,2)
an
d i
s p
erp
end
icu
lar
to t
he
grap
h o
f 2x
�3y
�9.
Fin
d th
e sl
ope
of 2
x�
3y�
9.2x
�3y
�9
Orig
inal
equ
atio
n
�3y
��
2x�
9S
ubtr
act
2xfr
om e
ach
side
.
y�
x�
3D
ivid
e ea
ch s
ide
by �
3.
Th
e sl
ope
of y
�x
�3
is
.So,
the
slop
e of
th
e li
ne
pass
ing
thro
ugh
(�
4,2)
th
at i
s 2 � 3
2 � 3
2 � 3Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Geo
met
ry:P
aral
lel a
nd
Per
pen
dic
ula
r L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
perp
endi
cula
r to
th
is l
ine
is t
he
neg
ativ
e re
cipr
ocal
of
,or
�.
Use
th
e po
int-
slop
e fo
rm t
o fi
nd
the
equ
atio
n.
y�
y 1�
m(x
�x 1
)P
oint
-slo
pe f
orm
y�
2 �
�(x
�(�
4))
m�
�;
(x1,
y1)
�(�
4, 2
)
y�
2 �
�(x
�4)
Sim
plify
.
y�
2 �
�x
�6
Dis
trib
utiv
e P
rope
rty
y�
�x
�4
Slo
pe-in
terc
ept
form
Wri
te t
he
slop
e-in
terc
ept
form
for
an
eq
uat
ion
of
the
lin
e th
at p
asse
s th
rou
gh t
he
give
n p
oin
t an
d i
s p
erp
end
icu
lar
to t
he
grap
h o
f ea
ch e
qu
atio
n.
1.(4
,2),
y�
x�
12.
(2,�
3),y
��
x�
43.
(6,4
),y
�7x
�1
y�
�2x
�10
y�
x�
6y
��
x�
4.(�
8,�
7),y
��
x�
85.
(6,�
2),y
��
3x�
66.
(�5,
�1)
,y�
x�
3
y�
x�
1y
�x
�4
y�
�x
�3
7.(�
9,�
5),y
��
3x�
18.
(�1,
3),2
x�
4y�
129.
(6,�
6),3
x�
y�
6
y�
x�
2y
�2x
�5
y�
�x
�4
10.F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
�2
and
is p
erpe
ndi
cula
r to
th
egr
aph
of
the
lin
e x
�2y
�5.
y�
�2x
�2
11.F
ind
an e
quat
ion
of
the
lin
e th
at h
as a
y-i
nte
rcep
t of
5 a
nd
is p
erpe
ndi
cula
r to
th
e gr
aph
of t
he
lin
e 4x
�3y
�8.
y�
x�
53 � 4
1 � 31 � 3
2 � 51 � 3
5 � 234 � 71 � 7
3 � 2
2 � 31 � 2
3 � 23 � 23 � 2
3 � 2
3 � 2
3 � 22 � 3
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Geo
met
ry:P
aral
lel a
nd
Per
pen
dic
ula
r L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
3G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
par
alle
l to
th
e gr
aph
of
each
eq
uat
ion
.
1.2.
3.
y�
2x�
1y
��
xy
�x
�3
4.(3
,2),
y�
3x�
45.
(�1,
�2)
,y�
�3x
�5
6.(�
1,1)
,y�
x�
4
y�
3x�
7y
��
3x�
5y
�x
�2
7.(1
,�3)
,y�
�4x
�1
8.(�
4,2)
,y�
x�
39.
(�4,
3),y
�x
�6
y�
�4x
�1
y�
x�
6y
�x
�5
10.(
4,1)
,y�
�x
�7
11.(
�5,
�1)
,2y
�2x
�4
12.(
3,�
1),3
y�
x�
9
y�
�x
�2
y�
x�
4y
�x
�2
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
each
eq
uat
ion
.
13.(
�3,
�2)
,y�
x�
214
.(4,
�1)
,y�
2x�
415
.(�
1,�
6),x
�3y
�6
y�
�x
�5
y�
�x
�1
y�
3x�
3
16.(
�4,
5),y
��
4x�
117
.(�
2,3)
,y�
x�
418
.(0,
0),y
�x
�1
y�
x�
6y
��
4x�
5y
��
2x
19.(
3,�
3),y
�x
�5
20.(
�5,
1),y
��
x�
721
.(0,
�2)
,y�
�7x
�3
y�
�x
�1
y�
x�
4y
�x
�2
22.(
2,3)
,2x
�10
y�
323
.(�
2,2)
,6x
�3y
��
924
.(�
4,�
3),8
x�
2y�
16
y�
5x�
7y
�x
�3
y�
�x
�4
1 � 41 � 2
1 � 73 � 5
4 � 3
5 � 33 � 4
1 � 4
1 � 21 � 4
1 � 2
1 � 31 � 4
1 � 4
1 � 2
1 � 2
1 � 2
( –2,
2)
x
y O
y �
1 2x �
1( 1
, –1)
x
y
O
y �
–x
� 3
( –2,
–3)
x
y O
y �
2x
� 1
©G
lenc
oe/M
cGra
w-H
ill31
4G
lenc
oe A
lgeb
ra 1
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
par
alle
l to
th
e gr
aph
of
each
eq
uat
ion
.
1.(3
,2),
y�
x�
52.
(�2,
5),y
��
4x�
23.
(4,�
6),y
��
x�
1
y�
x�
1y
��
4x�
3y
��
x�
3
4.(5
,4),
y�
x�
25.
(12,
3),y
�x
�5
6.(3
,1),
2x�
y�
5
y�
x�
2y
�x
�13
y�
�2x
�7
7.(�
3,4)
,3y
�2x
�3
8.(�
1,�
2),3
x�
y�
59.
(�8,
2),5
x�
4y�
1
y�
x�
6y
�3x
�1
y�
x�
12
10.(
�1,
�4)
,9x
�3y
�8
11.(
�5,
6),4
x�
3y�
112
.(3,
1),2
x�
5y�
7
y�
�3x
�7
y�
�x
�y
��
x�
Wri
te t
he
slop
e-in
terc
ept
form
of
an e
qu
atio
n o
f th
e li
ne
that
pas
ses
thro
ugh
th
egi
ven
poi
nt
and
is
per
pen
dic
ula
r to
th
e gr
aph
of
each
eq
uat
ion
.
13.(
�2,
�2)
,y�
�x
�9
14.(
�6,
5),x
�y
�5
15.(
�4,
�3)
,4x
�y
�7
y�
3x�
4y
��
x�
1y
�x
�2
16.(
0,1)
,x�
5y�
1517
.(2,
4),x
�6y
�2
18.(
�1,
�7)
,3x
�12
y�
�6
y�
5x�
1y
��
6x�
16y
�4x
�3
19.(
�4,
1),4
x�
7y�
620
.(10
,5),
5x�
4y�
821
.(4,
�5)
,2x
�5y
��
10
y�
x�
8y
�x
�3
y�
�x
�5
22.(
1,1)
,3x
�2y
��
723
.(�
6,�
5),4
x�
3y�
�6
24.(
�3,
5),5
x�
6y�
9
y�
x�
y�
x�
y�
�x
�
25.G
EOM
ETRY
Qu
adri
late
ral
AB
CD
has
dia
gon
als
A�C�
and
B�D�
.D
eter
min
e w
het
her
A �C�
is p
erpe
ndi
cula
r to
B�D�
.Exp
lain
.
Yes;
they
are
per
pen
dic
ula
r b
ecau
se t
hei
r sl
op
es a
re
7 an
d �
,wh
ich
are
neg
ativ
e re
cip
roca
ls.
26.G
EOM
ETRY
Tri
angl
e A
BC
has
ver
tice
s A
(0,4
),B
(1,2
),an
d C
(4,6
).D
eter
min
e w
het
her
tri
angl
e A
BC
is a
rig
ht
tria
ngl
e.E
xpla
in.
Yes;
sid
es A�
B�an
d A�
C�ar
e p
erp
end
icu
lar
bec
ause
th
eir
slo
pes
are
�2
and
,w
hic
h a
re n
egat
ive
reci
pro
cals
.1 � 2
1 � 7
x
y O
A
D
C
B
7 � 56 � 5
1 � 23 � 4
1 � 32 � 3
5 � 24 � 5
7 � 4
1 � 4
1 � 3
11 � 52 � 5
2 � 34 � 3
5 � 42 � 3
4 � 32 � 5
4 � 32 � 5
3 � 4
3 � 4
Pra
ctic
e (
Ave
rag
e)
Geo
met
ry:P
aral
lel a
nd
Per
pen
dic
ula
r L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csG
eom
etry
:P
aral
lel a
nd
Per
pen
dic
ula
r L
ines
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
©G
lenc
oe/M
cGra
w-H
ill31
5G
lenc
oe A
lgeb
ra 1
Lesson 5-6
Pre-
Act
ivit
yH
ow c
an y
ou d
eter
min
e w
het
her
tw
o li
nes
are
par
alle
l?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-6
at
the
top
of p
age
292
in y
our
text
book
.
•W
hat
is
a fa
mil
y of
gra
phs?
A g
rou
p o
f g
rap
hs
that
hav
e at
leas
to
ne
char
acte
rist
ic in
co
mm
on
,su
ch a
s sl
op
e o
r y-
inte
rcep
t.
•D
o yo
u t
hin
k li
nes
th
at d
o n
ot a
ppea
r to
in
ters
ect
are
para
llel
or
perp
endi
cula
r?p
aral
lel
Rea
din
g t
he
Less
on
1.R
efer
to
the
Key
Con
cept
box
on
pag
e 29
2.W
hy
does
th
e de
fin
itio
n u
se t
he
term
non
vert
ical
wh
en t
alki
ng
abou
t li
nes
wit
h t
he
sam
e sl
ope?
Ver
tica
l lin
es h
ave
slo
pes
th
at a
re u
nd
efin
ed s
o w
e ca
nn
ot
say
they
hav
e th
e sa
me
slo
pe.
2.W
hat
is
a ri
ght
angl
e?S
amp
le a
nsw
ers:
A r
igh
t an
gle
is o
ne
that
mea
sure
s90
°.It
is a
n a
ng
le f
orm
ed b
y p
erp
end
icu
lar
lines
.
3.R
efer
to
the
Key
Con
cept
box
on
pag
e 29
3.D
escr
ibe
how
you
fin
d th
e op
posi
te r
ecip
roca
lof
a n
um
ber.
Sam
ple
an
swer
:Th
e re
cip
roca
l of
a g
iven
nu
mb
er is
th
en
um
ber
fo
rmed
wh
en y
ou
sw
itch
th
e n
um
erat
or
and
den
om
inat
or.
Th
enyo
u g
ive
it t
he
op
po
site
sig
n o
f th
e o
rig
inal
nu
mb
er.
4.W
rite
th
e op
posi
te r
ecip
roca
l of
eac
h n
um
ber.
a.2
�b
.�
3c.
�d
.�
5
Hel
pin
g Y
ou
Rem
emb
er
5.O
ne
way
to
rem
embe
r h
ow s
lope
s of
par
alle
l li
nes
are
rel
ated
is
to s
ay “
sam
e di
rect
ion
,sa
me
slop
e.”
Try
to
thin
k of
a p
hra
se t
o h
elp
you
rem
embe
r th
at p
erpe
ndi
cula
r li
nes
hav
e sl
opes
th
at a
re o
ppos
ite
reci
proc
als.
Sam
ple
an
swer
:N
icel
y ri
gh
t an
gle
s fo
rmed
,use
op
po
site
rec
ipro
cals
.
1 � 513 � 12
12 � 131 � 3
1 � 2
©G
lenc
oe/M
cGra
w-H
ill31
6G
lenc
oe A
lgeb
ra 1
Pen
cils
of
Lin
esA
ll o
f th
e li
nes
th
at p
ass
thro
ugh
a
sin
gle
poin
t in
th
e sa
me
plan
e ar
e ca
lled
a p
enci
l of
lin
es.
All
lin
es w
ith
th
e sa
me
slop
e,bu
t di
ffer
ent
inte
rcep
ts,a
re a
lso
call
ed a
“pe
nci
l,”a
pen
cil o
f p
aral
lel l
ines
.
Gra
ph
som
e of
th
e li
nes
in
eac
h p
enci
l.
1.A
pen
cil
of l
ines
th
rou
gh t
he
2.A
pen
cil
of l
ines
des
crib
ed b
y po
int
(1,3
)y
�4
�m
(x�
2),w
her
e m
is a
ny
real
nu
mbe
r
3.A
pen
cil
of l
ines
par
alle
l to
th
e li
ne
4.A
pen
cil
of l
ines
des
crib
ed b
y x
�2y
�7
y�
mx
�3m
�2
x
y
Ox
y
O
x
y
Ox
y
O
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-6
5-6
Answers (Lesson 5-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sca
tter
Plo
ts a
nd
Lin
es o
f F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill31
7G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Inte
rpre
t Po
ints
on
a S
catt
er P
lot
A s
catt
er p
lot
is a
gra
ph i
n w
hic
h t
wo
sets
of
data
are
plo
tted
as
orde
red
pair
s in
a c
oord
inat
e pl
ane.
If y
incr
ease
s as
xin
crea
ses,
ther
e is
a p
osit
ive
corr
elat
ion
betw
een
xan
d y.
If y
decr
ease
s as
xin
crea
ses,
ther
e is
a n
egat
ive
corr
elat
ion
betw
een
xan
d y.
If x
and
yar
e n
ot r
elat
ed,t
her
e is
no
corr
elat
ion
.
EAR
NIN
GS
Th
e gr
aph
at
the
righ
t sh
ows
the
amou
nt
of m
oney
Car
men
ear
ned
eac
hw
eek
an
d t
he
amou
nt
she
dep
osit
ed i
n h
er s
avin
gsac
cou
nt
that
sam
e w
eek
.Det
erm
ine
wh
eth
er t
he
grap
h s
how
s a
pos
itiv
e co
rrel
atio
n,a
neg
ativ
eco
rrel
atio
n,o
r n
o co
rrel
atio
n.I
f th
ere
is a
p
osit
ive
or n
egat
ive
corr
elat
ion
,des
crib
e it
sm
ean
ing
in t
he
situ
atio
n.
The
gra
ph s
how
s a
posi
tive
cor
rela
tion
.The
mor
e C
arm
en e
arns
,the
mor
e sh
e sa
ves.
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
elat
ion
,a n
egat
ive
corr
elat
ion
,or
no
corr
elat
ion
.If
ther
e is
a p
osit
ive
corr
elat
ion
,des
crib
e it
.
1.2.
no
co
rrel
atio
nN
egat
ive
corr
elat
ion
;as
tim
e
incr
ease
s,sp
eed
dec
reas
es.
3.4.
Po
siti
ve c
orr
elat
ion
;as
th
e P
osi
tive
co
rrel
atio
n;
as t
he
nu
mb
er o
f ye
ars
incr
ease
s,th
e n
um
ber
of
year
s in
crea
ses,
the
nu
mb
er o
f cl
ub
s in
crea
ses.
nu
mb
er o
f fu
nd
s in
crea
ses.
Nu
mb
er
of
Mu
tual
Fun
ds
Year
s Si
nce
199
1
Number of Funds(thousands)
02
41
35
67
7 6 5 4 3
Sour
ce: T
he W
all S
treet
Jour
nal A
lman
ac
Gro
wth
of
Invest
men
t C
lub
s
Year
s Si
nce
199
0
Number of Clubs(thousands)
02
41
35
67
8
35 28 21 14 7
Sour
ce: T
he W
all S
treet
Jour
nal A
lman
ac
Avera
ge J
og
gin
g S
peed
Min
ute
s
Miles per Hour
010
205
1525
10 5
Avera
ge W
eekly
Wo
rk H
ou
rs i
n U
.S.
Year
s Si
nce
199
0
Hours
02
46
17
89
x
y
35
34.8
34.6
34.4
34.2
Sour
ce: T
he W
orld
Alm
anac
Carm
en
’s E
arn
ing
s an
d S
avin
gs
Do
llars
Ear
ned
Dollars Saved
040
8012
0
35 30 25 20 15 10 5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
©G
lenc
oe/M
cGra
w-H
ill31
8G
lenc
oe A
lgeb
ra 1
Lin
es o
f Fi
t
Th
e ta
ble
bel
ow s
how
s th
e n
um
ber
of
stu
den
ts p
er c
omp
ute
r in
Un
ited
Sta
tes
pu
bli
c sc
hoo
ls f
or c
erta
in s
choo
l ye
ars
from
199
0 to
200
0.
Year
1990
1992
1994
1996
1998
2000
Stu
den
ts p
er C
om
pu
ter
2218
1410
6.1
5.4
a.D
raw
a s
catt
er p
lot
and
det
erm
ine
wh
at
rela
tion
ship
exi
sts,
if a
ny.
Sin
ce y
decr
ease
s as
xin
crea
ses,
the
corr
elat
ion
is
neg
ativ
e.
b.
Dra
w a
lin
e of
fit
for
th
e sc
atte
r p
lot.
Dra
w a
lin
e th
at p
asse
s cl
ose
to m
ost
of t
he
poin
ts.A
lin
e of
fit
is
show
n.
c.W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
.T
he
lin
e of
fit
sh
own
pas
ses
thro
ugh
(1
993,
16)
and
(199
9,5.
7).F
ind
the
slop
e.
m�
m�
�1.
7
Fin
d b
in y
��
1.7x
�b.
16 �
�1.
7 �
1993
�b
3404
�b
Th
eref
ore,
an e
quat
ion
of
a li
ne
of f
it i
s y
��
1.7x
�34
04.
Ref
er t
o th
e ta
ble
for
Exe
rcis
es 1
–3.
1.D
raw
a s
catt
er p
lot.
3.W
rite
th
e sl
ope-
inte
rcep
t
2.D
raw
a l
ine
of f
it f
or t
he
data
.fo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
.
Th
e p
oin
ts (
0,11
.43)
and
(2,
12.2
8) g
ive
y�
0.42
5x�
11.4
3 as
a
line
of
fit.
U.S
. Pro
du
ctio
nW
ork
ers
Ho
url
y W
ag
e
Year
s Si
nce
199
5
Hourly Wage (dollars)
01
32
45
67
14 13 12 11
Sour
ce: T
he W
orld
Alm
anac
Year
sH
ou
rly
Sin
ce 1
995
Wag
e
0$1
1.43
1$1
1.82
2$1
2.28
3$1
2.78
4$1
3.24
5.7
�16
��
1999
�19
93
Stu
den
ts p
er
Co
mp
ute
rin
U.S
. Pu
bli
c Sch
oo
ls
Year
Students per Computer
1990
1992
1994
1996
1998
2000
24 20 16 12 8 4 0
Sour
ce: T
he W
orld
Alm
anac
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sca
tter
Plo
ts a
nd
Lin
es o
f F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sta
tist
ics:
Sca
tter
Plo
ts a
nd
Lin
es o
f F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill31
9G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
ela
tion
,a n
ega
tive
corr
ela
tion
,or
no
corr
ela
tion
.If
ther
e is
a p
osit
ive
or n
egat
ive
corr
elat
ion
,d
escr
ibe
its
mea
nin
g in
th
e si
tuat
ion
.
1.2.
Po
siti
ve;
the
lon
ger
th
e ex
erci
se,
no
co
rrel
atio
nth
e m
ore
Cal
ori
es b
urn
ed.
3.4.
Neg
ativ
e;as
wei
gh
t in
crea
ses,
Neg
ativ
e;as
th
e ye
ar in
crea
ses,
the
nu
mb
er o
f re
pet
itio
ns
the
nu
mb
er o
f ev
enin
g
dec
reas
es.
new
spap
ers
dec
reas
es.
BA
SEB
ALL
For
Exe
rcis
es 5
–7,u
se t
he
scat
ter
plo
t th
at s
how
s th
e av
erag
e p
rice
of
a m
ajor
-lea
gue
bas
ebal
l ti
cket
fro
m 1
991
to 2
000.
5.D
eter
min
e w
hat
rel
atio
nsh
ip,i
f an
y,ex
ists
in
th
e da
ta.E
xpla
in.
Po
siti
ve c
orr
elat
ion
;as
the
year
incr
ease
s,th
e p
rice
incr
ease
s.6.
Use
th
e po
ints
(19
93,9
.60)
an
d (1
998,
13.6
0)
to w
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
nfo
r th
e li
ne
of f
it s
how
n i
n t
he
scat
ter
plot
.y
�0.
8x�
1584
.87.
Pre
dict
th
e pr
ice
of a
tic
ket
in 2
004.
abo
ut
$18.
40
Base
ball
Tic
ket
Pri
ces
Year
Average Price ($)
’91
’92
’93
’94
’95
’96
’97
’98
’99
18 16 14 12 10 8 0’0
0
Sour
ce: T
eam
Mar
ketin
g Re
port,
Chi
cago
Even
ing
New
spap
ers
Year
Number of Newspapers
’91
’92
’93
’94
’95
’96
’97
’98
’99
1050
1000 950
900
850
800
750 0
Sour
ce: E
dito
r & P
ublis
her
Weig
ht-
Lift
ing
Wei
gh
t (p
ou
nd
s)
Repetitions
040
8020
6010
012
014
0
14 12 10 8 6 4 2
Lib
rary
Fin
es
Bo
oks
Bo
rro
wed
Fines (dollars)
02
45
67
88
13
10
7 6 5 4 3 2 1
Calo
ries
Bu
rned
Du
rin
g E
xerc
ise
Tim
e (m
inu
tes)
Calories
020
4010
3050
60
600
500
400
300
200
100
©G
lenc
oe/M
cGra
w-H
ill32
0G
lenc
oe A
lgeb
ra 1
Det
erm
ine
wh
eth
er e
ach
gra
ph
sh
ows
a p
osit
ive
corr
ela
tion
,a n
ega
tive
corr
ela
tion
,or
no
corr
ela
tion
.If
ther
e is
a p
osit
ive
or n
egat
ive
corr
elat
ion
,d
escr
ibe
its
mea
nin
g in
th
e si
tuat
ion
.
1.2.
no
co
rrel
atio
nP
osi
tive
;as
the
mea
n e
leva
tio
nin
crea
ses,
the
hig
hes
t p
oin
t in
crea
ses.
DIS
EASE
For
Exe
rcis
es 3
–6,u
se t
he
tab
le t
hat
sh
ows
the
nu
mb
er o
f ca
ses
of m
um
ps
in t
he
Un
ited
Sta
tes
for
the
year
s 19
95 t
o 19
99.
3.D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
re
lati
onsh
ip,i
f an
y,ex
ists
in
th
e da
ta.
Sour
ce:C
ente
rs fo
r Dise
ase
Cont
rol a
nd P
reve
ntio
n
Neg
ativ
e co
rrel
atio
n;
as t
he
year
in
crea
ses,
the
nu
mb
er o
f ca
ses
dec
reas
es.
4.D
raw
a l
ine
of f
it f
or t
he
scat
ter
plot
.S
amp
le a
nsw
er:
Use
(19
96,7
51),
(199
7,68
3).
5.W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or t
he
line
of
fit.
Sam
ple
an
swer
:y�
�68
x�
136,
479
6.P
redi
ct t
he
nu
mbe
r of
cas
es i
n 2
004.
abo
ut
207
ZOO
SF
or E
xerc
ises
7–1
0,u
se t
he
tab
le t
hat
sh
ows
the
aver
age
and
max
imu
m l
onge
vity
of
vari
ous
anim
als
in c
apti
vity
.
7.D
raw
a s
catt
er p
lot
and
dete
rmin
e w
hat
re
lati
onsh
ip,i
f an
y,ex
ists
in
th
e da
ta.
Sour
ce: W
alke
r’s M
amm
als o
f the
Wor
ld
Po
siti
ve c
orr
elat
ion
;as
th
e av
erag
e
incr
ease
s,th
e m
axim
um
incr
ease
s.8.
Dra
w a
lin
e of
fit
for
th
e sc
atte
r pl
ot.
Sam
ple
an
swer
:U
se (
15,4
0),(
35,7
0).
9.W
rite
th
e sl
ope-
inte
rcep
t fo
rm o
f an
equ
atio
n f
or t
he
lin
e of
fit
.S
amp
le a
nsw
er:
y�
1.5x
�17
.510
.Pre
dict
th
e m
axim
um
lon
gevi
ty f
or a
n a
nim
al w
ith
an
ave
rage
lon
gevi
ty o
f 33
yea
rs.
abo
ut
67 y
r
An
imal
Lon
gevit
y (
Years
)
Ave
rag
e
Maximum
50
1015
2025
3035
4045
80 70 60 50 40 30 20 10
Lo
ng
evit
y (y
ears
)
Avg
.12
2515
835
4041
20
Max
.47
5040
2070
7761
54
U.S
. M
um
ps
Case
s
Year
Cases
1995
1997
1999
2001
1000 800
600
400
200 0
U.S
.Mu
mp
s C
ases
Year
1995
1996
1997
1998
1999
Cas
es90
675
168
366
638
7
Sta
te E
levati
on
s
Mea
n E
leva
tio
n (
feet
)
Highest Point(thousands of feet)
1000
020
0030
00
16 12 8 4
Sour
ce: U
.S. G
eolo
gica
l Sur
vey
Tem
pera
ture
vers
us
Rain
fall
Ave
rag
e A
nn
ual
Rai
nfa
ll (i
nch
es)
AverageTemperature (�F)
1015
2025
3035
4045
64 60 56 52 0
Sour
ce: N
atio
nal O
cean
ic an
d At
mos
pher
ic Ad
min
istra
tion
Pra
ctic
e (
Ave
rag
e)
Sta
tist
ics:
Sca
tter
Plo
ts a
nd
Lin
es o
f F
it
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
tati
stic
s:S
catt
er P
lots
an
d L
ines
of
Fit
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
©G
lenc
oe/M
cGra
w-H
ill32
1G
lenc
oe A
lgeb
ra 1
Lesson 5-7
Pre-
Act
ivit
yH
ow d
o sc
atte
r p
lots
hel
p i
den
tify
tre
nd
s in
dat
a?
Rea
d th
e in
trod
uct
ion
to
Les
son
5-7
at
the
top
of p
age
298
in y
our
text
book
.
•W
hat
doe
s th
e ph
rase
lin
ear
rela
tion
ship
mea
n t
o yo
u?
Sam
ple
answ
er:
It m
ean
s th
at w
hen
yo
u g
rap
h t
he
dat
a p
oin
ts o
n a
coo
rdin
ate
gri
d,t
he
po
ints
all
lie o
n o
r cl
ose
to
a li
ne
that
you
co
uld
dra
w o
n t
he
gri
d.
•W
rite
th
ree
orde
red
pair
s th
at f
it t
he
desc
ript
ion
as
x in
crea
ses,
yd
ecre
ases
.S
amp
le a
nsw
er:
{(2,
5),(
3,3)
,(4,
1)}
Rea
din
g t
he
Less
on
1.L
ook
up
the
wor
d sc
atte
rin
a d
icti
onar
y.H
ow d
oes
this
def
init
ion
com
pare
to
the
term
scat
ter
plot
?O
ne
def
init
ion
sta
tes
“to
occ
ur
or
fall
irre
gu
larl
y o
r at
ran
do
m.”
Th
e p
oin
ts in
a s
catt
er p
lots
usu
ally
do
no
t fo
llow
an
exa
ctlin
ear
pat
tern
,bu
t fa
ll ir
reg
ula
rly
on
th
e co
ord
inat
e p
lan
e.
2.W
hat
is
a li
ne
of f
it?
How
man
y da
ta p
oin
ts f
all
on t
he
lin
e of
fit
?A
lin
e o
f fi
t sh
ow
sth
e tr
end
of
the
dat
a.It
is im
po
ssib
le t
o s
ay h
ow
man
y d
ata
po
ints
may
fall
on
a li
ne
of
fit—
may
be
seve
ral,
may
be
no
ne.
3.W
hat
is
lin
ear
inte
rpol
atio
n?
How
can
you
dis
tin
guis
h i
t fr
om l
inea
r ex
trap
olat
ion
?L
inea
r in
terp
ola
tio
n is
th
e p
roce
ss o
f p
red
icti
ng
a y
-val
ue
for
a g
iven
x-
valu
e th
at li
es b
etw
een
th
e le
ast
and
gre
ates
t x-
valu
es in
th
e d
ata
set.
“In
ter-
”m
ean
s b
etw
een
an
d “
extr
a-”
mea
ns
bey
on
d.I
f th
e x-
valu
e is
bet
wee
n t
he
extr
emes
of
the
x-va
lues
in t
he
dat
a se
t,yo
u s
ayin
terp
ola
tio
n;
if t
he
x-va
lue
is le
ss t
han
or
gre
ater
th
an t
he
extr
emes
,yo
u s
ay e
xtra
po
lati
on
.
Hel
pin
g Y
ou
Rem
emb
er
4.H
ow c
an y
ou r
emem
ber
wh
eth
er a
set
of
data
poi
nts
sh
ows
a po
siti
ve c
orre
lati
on o
r a
neg
ativ
e co
rrel
atio
n?
If it
loo
ks li
ke a
lin
e o
f fi
t fo
r th
e p
oin
ts w
ou
ld h
ave
ap
osi
tive
slo
pe,
ther
e is
a p
osi
tive
co
rrel
atio
n.I
f it
loo
ks li
ke a
lin
e o
f fi
tw
ou
ld h
ave
a n
egat
ive
slo
pe,
ther
e is
a n
egat
ive
corr
elat
ion
.
©G
lenc
oe/M
cGra
w-H
ill32
2G
lenc
oe A
lgeb
ra 1
Lat
itu
de
and
Tem
per
atu
re
Th
e la
titu
de
of a
pla
ce o
n E
arth
is t
he
mea
sure
of
its
dist
ance
from
th
e eq
uat
or.W
hat
do
you
thin
k is
th
e re
lati
onsh
ip
betw
een
a c
ity’
s la
titu
de a
nd
its
Jan
uar
y te
mpe
ratu
re?
At
the
righ
t is
a t
able
con
tain
ing
the
lati
tude
s an
d Ja
nu
ary
mea
n t
empe
ratu
res
for
fift
een
U.S
.cit
ies.
Sam
ple
an
swer
s ar
e g
iven
.
Sour
ces:
www.
indo
.com
and
www
.nws
.noa
a.gov
/clim
atex
.htm
l
1.U
se t
he
info
rmat
ion
in
th
e ta
ble
to c
reat
e
a sc
atte
r pl
ot a
nd
draw
a l
ine
of b
est
fit
for
the
data
.
2.W
rite
an
equ
atio
n f
or t
he
lin
e of
fit
.Mak
e a
con
ject
ure
abo
ut
the
rela
tion
ship
be
twee
n a
cit
y’s
lati
tude
an
d it
s m
ean
Jan
uar
y te
mpe
ratu
re.
y�
�2.
39x
�12
1.86
;Th
e h
igh
erth
e la
titu
de,
the
low
er t
he
tem
per
atu
re.
3.U
se y
our
equ
atio
n t
o pr
edic
t th
e Ja
nu
ary
mea
n t
empe
ratu
re o
f Ju
nea
u,A
lask
a,w
hic
h h
as l
atit
ude
58:
23 N
.�
17.7
�F
4.W
hat
wou
ld y
ou e
xpec
t to
be
the
lati
tude
of
a ci
ty w
ith
a J
anu
ary
mea
n t
empe
ratu
re
of 1
5°F
?44
:42
N
5.W
as y
our
con
ject
ure
abo
ut
the
rela
tion
ship
bet
wee
n l
atit
ude
an
d te
mpe
ratu
re c
orre
ct?
Yes;
as t
he
lati
tud
e in
crea
ses,
the
tem
per
atu
re d
ecre
ases
.
6.R
esea
rch
th
e la
titu
des
and
tem
pera
ture
s fo
r ci
ties
in
th
e so
uth
ern
hem
isph
ere
inst
ead.
Doe
s yo
ur
con
ject
ure
hol
d fo
r th
ese
citi
es a
s w
ell?
Yes.
Lati
tud
e (�
N)
Temperature (�F)
70 60 50 40 30 20 10 0
�10T
L20
4060
1030
50
U.S
.Cit
yL
atit
ud
eJa
nu
ary
Mea
n T
emp
erat
ure
Alb
any,
New
Yor
k42
:40
N20
.7°F
Alb
uque
rque
, N
ew M
exic
o35
:07
N34
.3°F
Anc
hora
ge, A
lask
a61
:11
N14
.9°F
Birm
ingh
am, A
laba
ma
33:3
2 N
41.7
°F
Cha
rlest
on,
Sou
th C
arol
ina
32:4
7 N
47.1
°F
Chi
cago
, Ill
inoi
s41
:50
N21
.0°F
Col
umbu
s, O
hio
39:5
9 N
26.3
°F
Dul
uth,
Min
neso
ta46
:47
N7.
0°F
Fai
rban
ks, A
lask
a64
:50
N�
10.1
°F
Gal
vest
on, T
exas
29:1
4 N
52.9
°F
Hon
olul
u, H
awai
i21
:19
N72
.9°F
Las
Veg
as,
Nev
ada
36:1
2 N
45.1
°F
Mia
mi,
Flo
rida
25:4
7 N
67.3
°F
Ric
hmon
d, V
irgin
ia37
:32
N35
.8°F
Tucs
on, A
rizon
a32
:12
N51
.3°F
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
5-7
5-7
Answers (Lesson 5-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. D
C
D
B
C
A
D
B
B
A
A
7
D
D
A
B
A
B
B
B
C
C
C
A
D
C
B
D
D
A
C
B
An
swer
s
(continued on the next page)
Chapter 5 Assessment Answer Key Form 1 Form 2APage 323 Page 324 Page 325
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: �21
C
B
A
C
D
A
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A
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A
B
B
D
B
B
B
A
C
D
�137�
C
B
A
C
D
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C
B
C
Chapter 5 Assessment Answer Key Form 2A (continued) Form 2BPage 326 Page 327 Page 328
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: � � 1.2t � 1.8; 6 years
Sample answer: Using data points (20, 67) and(40, 87), y � x � 47; 82
Time Spent Studying(minutes)
Sco
re R
ecei
ved
(per
cen
t)
0
60
70
80
90
100
10 20 30 40 50
y � �23
�x � 4
y � �2x � 1
y � 3x � 10
12x � 7y � �16
y � 8 � �13
�(x � 2)
x � �6
y � �32
�x � �12
�
y
xO
y � �23
�x � 2
5x � 7y � 14
y � 0.10x � 28.75
d � 3t; 36 mi
y
xO
about �0.49
�25
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0
1
An
swer
s
Chapter 5 Assessment Answer Key Form 2CPage 329 Page 330
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:y � �
65
�x � 6
Sample answer:Using data points (30, 6.1) and(70, 4.7), y � �0.035x � 7.15;about 4.9
Age
Perc
ent
Spen
t o
nEn
tert
ain
men
t
3
4
5
6
30 40 50 60 70 80
y � ��14
�x � 4
y � �3x � 18
y � �34
�x � �54
�
2x � 3y � �1
y � �43
�(x � 3)
x � 5
y � �5x � 29
y
xO
y � ��23
�x � 2
x � y � 2
y � 2.50x � 4.95
�12
�h
y
xO
about ��13
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1
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0
Chapter 5 Assessment Answer Key Form 2DPage 331 Page 332
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 9
y � �0.5x � 2
Sample answer:y � 52.99 � 0.12(x � 200)
Sample answer:Using data points
(424, 466) and (460, 488) y � 0.6x � 211.6; about 479
Positive; a verbal scoreis closely associatedwith the math score
Verbal Score
Mat
h S
core
450
460
470
480
490
500
400420440460480
y � 5
y � �35
�x � 6
y � ��43
�x � 9
x � 3
y � 6
y � ��35
�x � �256�
y � �52
�x � 11
y � 3x � 8
y � 2 � ��23�x
2x � 3y � 6
y
xO
2x � y � 1
y � 1� ��35
�(x � 2)
60
y
xO
about 690 people/yr
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An
swer
sA
nsw
ers
Chapter 5 Assessment Answer Key Form 3Page 333 Page 334
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
Chapter 5 Assessment Answer KeyPage 335, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts of slope,various forms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of slope, variousforms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts of slope,various forms of a linear equation, graphing lines from anequation, scatter plots, correlation, and predicting data.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of most of the concepts ofslope, various forms of a linear equation, graphing linesfrom an equation, scatter plots, correlation, and predictingdata.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy the requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
1a. After drawing a graph, students shouldexplain that they can use the two pointson the graph to determine the slope.This can be done by counting squaresfor the rise and run of the line or byusing the coordinates of the points inthe slope formula.
1b. The slope is the value of m in the slope-intercept form y � mx � b. Bysubstituting the value of m and thecoordinates of one of the points for x andy, the value of b can be found and anequation written using m and b. Theslope and either ordered pair can beused to write the point-slope form of anequation. The standard form of anequation is an algebraic manipulation ofeither of the other two forms ofequations. See students’ equations forthe line drawn.
2a. In order to graph the line through (�2, 3) you need to know the slope ofthe line, another point on the line, orthe equation of the line.
2b. If you knew the slope of the line, youcould plot another point using the riseand run on a coordinate plane. If youknew another point, you could graphthat point and draw a line through (�2, 3) and the other point. If you knewthe equation of the line, you could usethe slope-intercept form of the equationto find the slope and intercept forgraphing or you could use the equationand substitution to find another pointon the line.
3a. The points have a strong negativecorrelation. This means that as xincreases, y decreases.
3b. One example is the longer a candleburns, the shorter it gets. Another is thelonger you run a car, the less gasoline isleft in the tank.
3c. See students’ work.
4a.
4b. While students’ knowledge from otherexperiences may lead them to thatconclusion, there may be other factorsthat contribute to increased longevity.The information on the graph only leadsus to claim that life expectancy isincreasing.
4c. A regression equation calculated by agraphing calculator would yield aprediction of 78.9 years. However,students may look at the era since 1980and notice that each 5-year period isabout 0.3 year less than the previous 5-year period increase. This patternwould yield a prediction of about 75.9years.
50
55
60
65
70
75
80
'20'30'40'50'60'70'80 '90 '00Year of Birth
Life
Exp
ecta
ncy
(yea
rs)
An
swer
s
Chapter 5 Assessment Answer Key Page 335, Open-Ended Assessment
Sample Answers
In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items.
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
1. perpendicular lines;parallel lines
2. constant ofvariation
3. scatter plot
4. family of graphs
5. rate of change
6. linear interpolation
7. slope
8. slope-intercept
9. point-slope
10. standard
11. Sample answer:A line of fit is a linethat comes close tothe data points for ascatter plot, even ifall the data pointsdo not lie on thatline.
12. Sample answer:Linear extrapolationis the process ofusing a linearequation to predicta y value for an x value that liesbeyond theextremes of thedomain of therelation.
1.
2.
3.
4.
5.
Quiz (Lessons 5–3 and 5–4)
Page 337
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lesson 5–7)
Page 338
1–2.
3.
4.
5. Sample answer: $35,850
Sample answer: Usingdata points (27, 19.1)
and (29, 25.8),y � 3.35x � 71.35
Positive; the older youget, the greater your
income.
Age
Med
ian
Inco
me
($10
00)
16
19
22
25
28
31
26 27 28 29 30
y � ��49
�x � 3
y � ��13
�x � �134�
y � 1 � 0
y � �x � 7
y � 6 � ��13
�(x � 3)
C
h � 3y � 48 for h ininches or h � 0.25y � 4
for h in feet
y
xO
y � ��141�x � �
5181�
y � �14
�x � 5
$285
5 students/yr
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Chapter 5 Assessment Answer Key Vocabulary Test/Review Quiz (Lessons 5–1 and 5–2) Quiz (Lessons 5–5 and 5–6)
Page 336 Page 337 Page 338
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
1.
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5.
6.
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10.
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12.
13.
14.
15.
16.
17.
18.y � �
53
�x � 4
x � �6
y � �3x � 12
�57
�
y � �32
�x � 2
Yes, exactly one memberof the range is paired
with each member of thedomain.
{�7.5, �6.5, �6,�5, �3.5}
�7
�89
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�2a � 3b
�30y
�15.1
�112�
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2�14
�
0
2r2s2
y � �13
�x � �23
�
�13
�
y � �3x � 2
y � x � 2
y � ��34
�x � 5
A
B
A
A
C
An
swer
s
Chapter 5 Assessment Answer Key Mid-Chapter Test Cumulative ReviewPage 339 Page 340
© Glencoe/McGraw-Hill A32 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
13. 14.
15.
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Page 341 Page 342