tanks a lot introduction to linear functions vocabulary 1 ......2011/10/31 · slope-intercept form...

Chapter 1 l Skills Practice 297

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Skills Practice Skills Practice for Lesson 1.1

Name _____________________________________________ Date ____________________

Tanks a Lot Introduction to Linear Functions

Vocabulary Define each term in your own words.

1. function

2. linear function

3. independent variable

4. dependent variable

5. variable

Problem Set Determine the independent quantity and the dependent quantity in each example.

1. A car is traveling at a rate of sixty miles per hour for several hours.

independent quantity: time in hours

dependent quantity: distance in miles

298 Chapter 1 l Skills Practice

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2. Sharon is growing at a rate of two inches per year.

3. The area of a square floor is the product of the length of two of its sides.

4. The perimeter of a square is the sum of the length of all four of its sides.

5. The length of a video file in minutes relates to the size of the file in bytes.

6. The total weight of a bag of apples in pounds relates to the number of apples in

the bag.

Define a variable to represent each of the quantities. Then write an equation that shows the relationship between the two variables.

7. A runner travels 4 miles per hour. Write an equation to show the relationship

between the total distance the runner travels and the time.

Let t represent the amount of time in hours.

Let d represent the distance the runner travels in miles.

d � 4t

8. Each DVD at an electronics store costs $12.50. Write an equation to show the relationship

between the total cost when purchasing DVDs and the number of DVDs.


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9. To make one solar panel, a company uses two kilograms of silicon. The company

has 100 kilograms of silicon. Write an equation to show the relationship between

the amount of silicon remaining and the number of solar panels made.

10. A bowling ball company uses seven pounds of resin to make one seven-pound bowling

ball. They have a total of 490 pounds of resin. Write an equation to show the relationship

between the amount of resin remaining and the number of seven-pound bowling

balls made.

11. Julia opens a bank account and deposits $500 into the account. Each month, she

deposits $50 into the account. Write an equation to show the relationship between

the total amount of money in her bank account and the number of months since

she opened the account.

12. A water tower contains 15,000 gallons of water. Each week, 2500 gallons of water

are used and 1000 gallons of water are added. Write an equation to show the

relationship between the total amount of water remaining in the water tower and

the number of weeks that have elapsed.


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Graph each linear function.

13. y � 2 x � 1 14. y � 3x � 2

15. y � � 1 __ 2 x � 2 16. y � 2 __

3 x � 1 __

2

17. y � �4x � 5 __ 4 18. y � 2x � 7 __

3

1

2

3

4

–1

–2

–3

–4

y

1 3 42–3–4 –2 –1 x0

y = 2x – 1


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Use the given information to answer each question.

19. The distance, d, in miles that a plane travels can be modeled by the equation d � 550t,

where t represents the time in hours. If the plane travels for 7 hours, how far will it go?

d � 550t

d � 550(7)

d � 3850

The plane will travel 3850 miles in 7 hours.

20. The distance, d, in feet that a fly travels can be modeled by the equation

d � 5t, where t represents the time in seconds. If the fly travels for 30 seconds,

how far will it have gone?

21. The equation w � 1,000,000 � 20m shows the amount of water, w, in gallons

remaining in a water tower, where m represents the number of minutes that have

passed. When will there be 750,000 gallons of water in the water tower?


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22. The equation a � 1750 � 50t shows the amount of money, a, in dollars remaining

in a bank account where t represents the time in weeks. When will the balance in

the account be $1000?

23. A ticket seller’s weekly earning, s, in dollars can be modeled by the equation

s � 0.10t � 350, where t represents the number of tickets he sells. How many

tickets will the ticket seller have to sell to make $440 that week?

24. The total number of computers, c, that a company can manufacture can be

modeled by the equation c � 1 ___ 50

s � 250, where s represents the number of

screws that they need to order. How many screws will they need to order so that

they can manufacture 525 computers?


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Name _____________________________________________ Date ____________________

Calculating Answers Solving Linear Equations and Linear Inequalities in One Variable

Vocabulary Write the term that best completes each statement.

1. The solution of an inequality can be graphed on a(n) .

2. Adding, subtracting, multiplying, and distributing are all examples of

that can be used to solve an equation.

3. Addition, subtraction, multiplication, and division are the four

basic that can be applied to both sides of a linear equation to

solve the equation.

4. A(n) is a statement that compares two expressions.

Problem Set Indicate which transformation(s) are needed to solve each equation.

1. x � 1 � 4 2. x � 3 � 2

Add 1 to both sides.

3. 2x � 4 4. x __ 4 � 7

5. 3x � 2 � 8 6. x __ 2 � 5 � 15


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S olve each equation.

7. x � 3 � 10 8. �3 � x � 1

x � 3 � 3 � 10 � 3

x � 7

9. 2x � 6 � 10 10. 3x � 9 � 27

11. x __ 2 � 3 � 1 12. � x __

3 � 2 � 4

13. � 2 __ 3

x � 3 � �1 14. 3 __ 5 x � 4 � �8


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15. 2 x � 15 � 5 � 3x 16. 4x � 3x � 9 � 2 x

S olve each inequality. Graph the solution on a number line.

17. 3x � 2 � 8 18. 2x � 5 � 7

3x � 2 � 2 � 8 � 2

3x � 6

3x ___ 3 � 6 __

3

x � 2

19. �4x � 3 � �13 20. 2 � 3x � 11

21. 2x � 3 � 5 22. �x � 4 � �13

1 3 4 52–3–4–5 –2 –1 0


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23. 2( x � 3) � 5 24. 4 � �3(2x � 5)

25. � x __ 2

� 3 � 4 26. 2 __ 3 x � 4 � 10


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Name _____________________________________________ Date ____________________

Running a 10K Slope-Intercept Form of Linear Functions

Vocabulary Determine each of the following for the linear function 2 x � 3y � 6.

1. slope 2. y-intercept

3. slope-intercept form 4. x-intercept

Problem Set Identify the slope of each linear function.

1. y � 2 x � 3 2. y � �3x � 4

The slope is 2.

3. y � � 2 __ 3 x � 1 __

2 4. y � 5 __

2 x � 2 __

5

Identify the y-intercept of each linear function.

5. y � �5x � 2 6. y � x � 3

The y-intercept is 2.

7. y � 2 __ 3 x � 1 __

2 8. y � � 3 __

2 x � 3 __

2


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Write a linear equation in slope-intercept form for each situation.

9. Louise opens a bank account and deposits $250. Every month she deposits $50 into her

account. Write an equation to represent the amount she has in her account after x months.

y � 50x � 250

10. Erin opens a bank account and deposits $350. Every month she withdraws $25

from her account. Write an equation to represent the amount she has in her

account after x months.

11. A computer is downloading a 100-megabyte program file. It downloads the

program at a rate of 5 megabytes per minute. Write an equation to represent the

number of megabytes left to download after x minutes.

12. Marco has 20 gigabytes of computer programs on his computer. Every month he

adds 1.5 gigabytes of programs to his computer. Write an equation to represent the

number of gigabytes of programs he has on his computer after x months.

Calculate the slope and y-intercept for each function.

13. A linear function passes through the points (0, 0) and (4, 8).

The y-intercept is 0.

m � y2 � y1 _______ x2 � x1

� 8 � 0 ______ 4 � 0

� 8 __ 4 � 2

The slope is 2.

14. A linear function passes through the points (0, 0) and (3, �27).


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15. A linear function passes through the points (�4, 9) and (3, 5).

16. A linear function passes through the points (�5, �2) and (3, 10).

17. A linear function passes through the points (3, 0) and (4, 2).


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18. A linear function passes through the points (�2, �6) and (�4, 0).

Graph each linear function using its slope and y-intercept.

19. y � x � 2 20. y � �2x � 3

Slope � 1

y-intercept � 2

1

2

3

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y

1 3 42–3–4 –2 –1 x

y = x + 2

0


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21. y � � 1 __ 2 x � 1 22. y � 3 __

2 x � 1

23. y � 4 24. y � �3


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Name _____________________________________________ Date ____________________

Pump It Up Standard Form of Linear Functions

Vocabulary Give an example of each key term.

1. standard form of a linear equation

2. slope-intercept form of a linear equation

Problem Set For each linear equation written in standard form, calculate the x- and y-intercepts. Use the intercepts to graph the equation.

1. x � y � 3 2. x � y � �2

x � 0 � 3 0 � y � 3

x � 3 y � 3

x-intercept � 3; y-intercept � 3

1

2

3 (0, 3)

(3, 0)

4

–1

–2

–3

–4

y

1 3 42–3–4 –2 –1 x0


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3. 2x � 3y � 6 4. x � 2y � 4

5. �2x � 5y � 10 6. 3x � 4y � 12


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7. 2 x � y � 3 8. �x � 3y � 5

Rewrite each linear equation in slope-intercept form.

9. x � y � 2 10. �x � y � �1

y � �x � 2

11. 2x � y � 5 12. 2 x � y � 3

13. 2x � 3y � 12 14. 5x � 3y � 15

15. �3x � 2y � 1 16. �x � 5y � 10


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Rewrite each linear equation in standard form.

17. y � 2 x � 3 18. y � �4x � 5

�2 x � y � �3

19. y � 1 __ 3 x � 4 20. y � � 2 __

3 x � 1

21. y � � 5 __ 4 x � 1 __

6 22. y � 4 ___

15 x � 5 __

9


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Name _____________________________________________ Date ____________________

Shifts and Flips Basic Functions and Linear Transformations

Vocabulary Write the term that best completes each statement.

1. A function undergoes a(n) when it is stretched or shrunk.

2. A(n) is a line in which a function is flipped so that it mirrors itself.

3. A(n) is a transformation in which a function is flipped over a given line.

4. The function y � x is the of the function y � 2 x � 3.

Problem Set Indicate the algebraic transformation which was performed on the basic function to result in each transformed function.

1. y � x � 2 2. y � x � 1

Add 2.

3. y � �4x 4. y � 1 __ 5 x

Indicate the graphical transformation(s) which were performed on the basic function to result in each transformed function.

5. y � x � 3

Move the graph down 3 units.

6. y � x � 1

7. y � 2 x � 3

8. y � �3x � 4


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9. y � � 1 __ 2 x � 3

10. y � 5 __ 3 x � 4

Graph each set of equations on the same grid. Compare the graphs of the lines. Then determine whether the graphs of the lines are parallel, perpendicular, or neither.

11. y � x � 3 and y � x � 1 12. y � 2 x and y � 4x

The first graph is shifted two units up from the second graph. The lines

are parallel.

1

2

3 y = x + 1

y = x + 3

4

–1

–2

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–4

y

1 3 42–3–4 –2 –1 x0


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13. y � �x and y � x � 2 14. y � 1 __ 2 x � 2 and y � �2x � 3

15. y � 2 __ 3 x � 2 and y � 2 __

3 x � 2 16. y � 1 __

4 x � 3 and y � 1 __

2 x � 1


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17. y � � 1 __ 5 x and y � 5x 18. y � �x � 2 and y � x � 2

19. y � �2 x � 1 and y � �2 x � 3. 20. y � 0 and y � 3


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Name _____________________________________________ Date ____________________

Inventory and Sand Determining the Equations of Linear Functions

Vocabulary Identify the similarities and differences between each pair of key terms.

1. point-slope form and two-point form

2. parallel lines and perpendicular lines

Problem Set Determine the slope-intercept form of the equation of each line.

1. Slope � 2 and y-intercept � 3 2. Slope � �4 and y-intercept � 10

y � 2 x � 3

3. Slope � �1 and y-intercept � �4 4. Slope � 1 and y-intercept � �12

Determine the slope-intercept form of the equation of each line.

5. Slope � �5 and the line passes 6. Slope � 10 and the line passes

through the point (2, 3) through the point (3, 5)

y � 3 � �5( x � 2)

y � 3 � �5x � 10

y � �5x � 13


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7. Slope � 7 and the line passes through 8. Slope � �3 and the line passes the

point (1, �4) through the point (5, �6)

Determine the slope-intercept form of the equation of the line passing through each pair of points.

9. (1, 2) and (5, 3) 10. (2, 6) and (5, 8)

m � 3 � 2 ______ 5 � 1

� 1 __ 4

y � 3 � 1 __ 4 ( x � 5)

y � 1 __ 4 x � 5 __

4 � 3

y � 1 __ 4 x � 7 __

4

11. (�2, 5) and (4, �3) 12. (1, �7) and (5, �3)

13. (0, 3) and (1, 3) 14. (2, 4) and (3, 4)


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Determine the slope-intercept form of the equation of each line, given the equation of a line parallel to the line and a point on the line.

15. y � 3x � 2, (1, 4) 16. y � 5x � 6, (3, 5)

4 � 3(1) � b

1 � b

y � 3x � 1

17. y � �2 x � 3, (�2, 6) 18. y � �4x � 1, (3, �4)

19. y � 1 __ 3 x � 11, (6, 5) 20. y � �3 __

2 x � 10, (4, �3)

Determine the slope-intercept form of the equation of each line, given the equation of a line perpendicular to the line and a point on the line.

21. y � 3x � 1, (2, 4) 22. y � 4x � 3, (1, 1)

m1 � � 1 ___ m2 � � 1 __

3

y � 4 � � 1 __ 3 ( x � 2)

y � � 1 __ 3 x � 2 __

3 � 4

y � � 1 __ 3 x � 14 ___

3


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23. y � 1 __ 3 x � 2, (3, �2) 24. y � �3 __

4 x � 9, (�5, 1)

25. y � �1 __ 5 x � 6, (0, 3) 26. y � 1 __

4 x � 2, (1, 0)


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Name _____________________________________________ Date ____________________

Absolutely! Absolute Value in Equations and Inequalities in One and Two Variables

Vocabulary Match each example with the term that describes it.

1. | x � 2| � 3 a. absolute value expression

2. |3x| b. absolute value equation

3. 2|3x � 1| � 2 � 5 c. absolute value inequality

4. 2 � 4x � 5 � 8 d. compound inequality

Problem Set Solve each equation.

1. |x � 3| � 4 2. |x � 2| � 5

x � 3 � �4

x � �3 � 4

x � �7, 1

3. |x � 1| � 2 � 7 4. |x � 3| � 4 � 10


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5. |2x � 3| � 8 6. |�x � 4| � 1

Graph each equation.

7. y � |x � 3| 8. y � |x � 2|

9. y � |3x � 6| 10. y � |4x � 16|

1

2

3

4

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–2

–3

–4

y

1 3 42–3–4 –2 –1 x

y = |x + 3|

0


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11. y � |�x � 3| 12. y � |2x � 8|

Solve each inequality and graph its solution on a number line.

13. |3x � 12| � 3 14. |4x � 22| � 2

3x � 12 � �3 or 3x � 12 � 3

3x � 9 or 3x � 15

x � 3 or x � 5

15. |�x � 3| � 5 16. |x � 10| 4

17. | 2 __ 3 x � 4 | � 2 18. | � 1 __

4 x � 2 | 1

6 8 9 107210 3 4 5


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Graph each inequality.

19. y � | x � 3| 20. y � | x � 1|

21. y |3x � 6| 22. y � |�x � 2|

23. y � |4x � 16| 24. y � |�3x � 12|

1

2

3

4

–1

–2

–3

–4

y

1 3 42–3–4 –2 –1 x

y > |x – 3|

0


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Inverses and Pieces Functional Notation, Inverses, and Piecewise Functions

Vocabulary Give an example of each term.

1. relation

2. domain

3. range

4. function

5. inverse operations

6. functional notation

7. identity function

8. inverse functions


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9. composition of functions

10. piecewise function

Problem Set Rewrite each linear function using functional notation.

1. y � 2x � 3 2. y � �3x � 1

f( x) � 2 x � 3

3. 2x � 3y � 6 4. 3x � 2y � 12

Calculate the value of each function for the given values of the independent variable.

5. f( x) � 2x, calculate f(�1) and f(2)

f(�1) � �2; f(2) � 4

6. f( x) � �x, calculate f(�3) and f(4)

7. k( x) � �3x � 5, calculate k(�5) and k(8)

8. k( x) � 4x � 2, calculate k(0) and k(6)

9. g( x) � x2 � 2x, calculate g(�3) and g(2)

10. g( x) � �2x2 � 3, calculate g(�1) and g(4)


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Determine the inverse of each function.

11. f( x) � �4x 12. f( x) � 2x

f�1( x) � � 1 __ 4

x

13. g( x) � 5x � 2 14. g( x) � �3x � 4

15. h( x) � 2.3x � 1.3 16. h( x) � �4.5x � 5.6

For the functions f( x) � x � 2 and g( x) � �3x, calculate each composition.

17. f(g(2)) 18. g(f(2))

f(g(2)) � f(�6) � �6 � 2 � �4

19. g(f(�3)) 20. f(g(�3))

21. f(f(2)) 22. g(g(2))

Graph each piecewise function.

23. f( x) � � 2x � 1 x � 2 �x � 4 x � 2

24. f( x) � � �x � 4 x �1

2x � 1 x � �1

1

2

3

4

5

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–3

y

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25. g( x) � � �x � 1 x � �1

2x �1 x 2 �x � 2 x � 2

26. g( x) � � x x �4 �2x � 3 �4 � x � 1 �x x � 1

Write a piecewise function to model each situation.

27. A rental car company charges $0.35 per mile for the first 200 miles. After 200 miles

they charge $0.20 per mile. Let c(m) be the cost for driving m miles.

c(m) � � 0.35m m � 200 0.2m m � 200

28. A laundromat charges $1.25 per pound of laundry for the first 10 pounds needed to

be cleaned. After 10 pounds they charge $0.75 per pound. Let c(l) be the cost for

cleaning l pounds of laundry.

29. A movie theatre charges $5.00 per ticket for people between the ages of 0 and

15 years. They charge $7.50 per ticket for people above the age of 15. Let c(a)

be the cost of a movie if a person’s age is a years.

30. A garage will inflate bicycle tires that are smaller than 20 inches in diameter for

$1.50. They charge $2.25 to inflate bicycle tires that are 20 inches or larger. Let

c(d ) be the cost to inflate a bicycle tire that has a diameter of d inches.


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31. A home-and-garden store charges $10.25 for a cubic yard of gravel if you buy

10 cubic yards or less. They charge $9.50 for a cubic yard of gravel if you buy

between 10 and 15 cubic yards. They charge $8.75 for a cubic yard of gravel if you

buy 15 cubic yards or more. Let c( y) be the cost of y cubic yards of gravel.

32. An airline charges different ticket prices based on the number of miles a plane

travels. If a plane travels less than 500 miles, an airline will charge $0.85 per mile.

If a plane travels 500 miles to 1500 miles, they charge $0.70 per mile. If a plane

travels more than 1500 miles, they charge $0.55 per mile. Let c(m) be the cost to fly

m miles.

tanks a lot introduction to linear functions vocabulary 1 ......2011/10/31 · slope-intercept form...

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