lesson 2.2 , for use with pages 82-88
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4 – 3. 1. 7 – 8. 8 – 8. 2. 3 – 5. Lesson 2.2 , For use with pages 82-88. Evaluate each expression. . –1. ANSWER. –0. ANSWER. 2 – 7. 3. 5 – 5. Lesson 2.2 , For use with pages 82-88. Evaluate each expression. undefined. ANSWER. - PowerPoint PPT PresentationTRANSCRIPT
Lesson 2.2, For use with pages 82-88
Evaluate each expression.
ANSWER –1
ANSWER –0
1. 4 – 37 – 8
2. 8 – 83 – 5
Evaluate each expression.
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4. An Internet company had a profit of $2.6 million in retail sales over the last five years. What was its average annual profit?
ANSWER $520,000
ANSWER
3. 2 – 75 – 5
Lesson 2.2, For use with pages 82-88
2.2 Finding Slope
Find slope in real lifeEXAMPLE 1
Skateboarding
A skateboard ramp has a rise of 15 inches and a run of 54 inches. What is its slope?
SOLUTION
slope = riserun =
ANSWER
The slope of the ramp is 518
.
518
=1554
Standardized Test PracticeEXAMPLE 2
SOLUTION
Let (x1, y1) = (–1, 3) and (x2, y2) = (2, –1).
m =y2 – y1
x2 – x1=
–1 – 32 – (–1) = 4
3
ANSWER
The correct answer is A.
for Examples 1 and 2GUIDED PRACTICE
1. What If ? In Example 1, suppose that the rise of the ramp is changed to 12 inches without changing the run. What is the slope of the ramp?
ANSWER
The slope of the ramp is 2 9
.
GUIDED PRACTICE
ANSWER
The correct answer is D.
2. What is the slope of the line passing through the points (–4, 9) and (–8, 3) ?
for Examples 1 and 2
GUIDED PRACTICE
Find the slope of the line passing through the given points.
3. (0, 3), (4, 8)
for Examples 1 and 2
ANSWER 54
4. (– 5, 1), (5, – 4)
ANSWER 12
–
6. (7, 3), (–1, 7)
ANSWER 12
–
5. (–3, –2), (6, 1)
ANSWER 13
Classify lines using slope
EXAMPLE 3
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
b. (–6, 0), (2, –4)
d. (4, 6), (4, –1)c. (–1, 3), (5, 8)
SOLUTION
a. (–5, 1), (3, 1)
1 – 13 – (–5) =m =a. Because m = 0, the line is
horizontal.–4 – 02 – (–6) =m =b. Because m < 0, the line
falls.
08 = 0
–48 =
12
–
Classify lines using slope
EXAMPLE 3
56
8 – 35– (–1) =m =c. Because m > 0, the line rises.
–7 0
–1 – 6 4 – 4 =m =d. Because m is undefined, the
line is vertical.
GUIDED PRACTICE for Example 3GUIDED PRACTICE
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
7. (–4, 3), (2, –6)
Because m < 0, the line falls.
ANSWER
8. (7, 1), (7, –1)
Because m is undefined, the line is vertical.
ANSWER
GUIDED PRACTICE for Example 3GUIDED PRACTICE
9. (3, –2), (5, –2)
Because m = 0, line is horizontal.
10. (5, 6), (1, –4)
Because m > 0 the line rises.
ANSWER ANSWER
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.
Classify parallel and perpendicular linesEXAMPLE 4
Tell whether the lines are parallel, perpendicular, orneither.
Line 1: through (–2, 2) and (0, –1)a.Line 2: through (–4, –1) and (2, 3)
Line 1: through (1, 2) and (4, –3)b.Line 2: through (–4, 3) and (–1, –2)
SOLUTION
Find the slopes of the two lines.a.
m1 =–1 – 20 – (–2) =
– 3 2
=32
–
Classify parallel and perpendicular lines
EXAMPLE 4
m2 =3 – (–1) 2 – (–4) =
4 6
=23
ANSWER
Because m1m2 = –2
3
3
2= –1, m1 and m2
are negative reciprocals of each other. So, the lines are perpendicular.
Classify parallel and perpendicular lines
EXAMPLE 4
Find the slopes of the two lines.b.
m1 =–3 – 2 4 – 1 =
–5 3
=53
–
m2 =–2 – 3 –1 – (–4) =
–5 3
=53
–
ANSWER
Because m1 = m2 (and the lines are different), you can conclude that the lines are parallel.
GUIDED PRACTICE for Example 4GUIDED PRACTICE
Tell whether the lines are parallel, perpendicular, or neither.
11. Line 1: through (–2, 8) and (2, –4)
Line 2: through (–5, 1) and (–2, 2)
ANSWER
12. Line 1: through (–4, –2) and (1, 7)
Line 2: through (–1, –4) and (3, 5)
ANSWER
perpendicular
neither
Solve a multi-step problem
EXAMPLE 5
Forestry
Use the diagram, which illustrates the growth of a giant sequoia, to find the average rate of change in the diameter of the sequoia over time. Then predict the sequoia’s diameter in 2065.
Solve a multi-step problemEXAMPLE 5
SOLUTIONSTEP 1Find the average rate of change.
141 in. – 137 in.2005 – 1965=
4 in. 40 years=
= 0.1 inch per year
Average rate of change Change in diameterChange in time=
Solve a multi-step problem
EXAMPLE 5
STEP 2Predict the diameter of the sequoia in 2065.Find the number of years from 2005 to 2065. Multiply this number by the average rate of change to find the total increase in diameter during the period 2005–2065.
Number of years = 2065 – 2005 = 60Increase in diameter =(60 years) (0.1 inch/year) = 6 inches
ANSWER
In 2065, the diameter of the sequoia will be about 141 + 6 = 147 inches.
GUIDED PRACTICE for Example 5GUIDED PRACTICE
13. What If ? In Example 5, suppose that the diameter of the sequoia is 248 inches in 1965 and 251 inches in 2005. Find the average rate of change in the diameter, and use it to predict the diameter in 2105.
ANSWER
The average rate of change is 0.075in. per year.
In 2105, the diameter of the sequoia will be about 258.5 inches.