Question

lesson 2 slope practice name: _____________ period: ____
find the slope of the line that passes through each pair of points.
1.
2.
3.

1. $(6, 3), (7, -4)$
2. $(-9, -3), (-7, -5)$
3. $(6, -2), (5, -4)$

7.
8.
9.

1. portraits paolos portraits charges $15 per photo with no sitting fee. the graph shows the fees for clear image studio. compare the functions by comparing their rates of change.

a. rate or slope for paolos portraits_________
b. rate or slope for clear image_________
c. which company has the greatest rate of change or slope? ______
clear image studio

1. toll roads the table shows the cost for traveling on a toll road in henderson. the graph shows the cost of traveling on a toll road in clarkson.

a. rate or slope for henderson toll road_________
b. rate or slope for clarkson toll road_________
c. which company has the greatest rate of change or slope? ______
henderson toll road costs
miles traveled | cost ($)
10 | 3
20 | 6
30 | 9
clarkson toll road costs
chapter 3

Explanation:

Step1: Recall slope formula

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
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Problem 1

Step1: Identify points

Points: $(-2,3), (-1,0)$

Step2: Calculate slope

$m=\frac{0-3}{-1-(-2)}=\frac{-3}{1}=-3$
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Problem 2

Step1: Identify points

Points: $(-2,-3), (3,1)$

Step2: Calculate slope

$m=\frac{1-(-3)}{3-(-2)}=\frac{4}{5}$
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Problem 3

Step1: Identify points

Points: $(-2,3), (3,3)$

Step2: Calculate slope

$m=\frac{3-3}{3-(-2)}=\frac{0}{5}=0$
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Problem 4

Step1: Identify points

Points: $(6,3), (7,-4)$

Step2: Calculate slope

$m=\frac{-4-3}{7-6}=\frac{-7}{1}=-7$
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Problem 5

Step1: Identify points

Points: $(-9,-3), (-7,-5)$

Step2: Calculate slope

$m=\frac{-5-(-3)}{-7-(-9)}=\frac{-2}{2}=-1$
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Problem 6

Step1: Identify points

Points: $(6,-2), (5,-4)$

Step2: Calculate slope

$m=\frac{-4-(-2)}{5-6}=\frac{-2}{-1}=2$
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Problem 7

Step1: Identify points

Points: $(0,1), (2,5)$

Step2: Calculate slope

$m=\frac{5-1}{2-0}=\frac{4}{2}=2$
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Problem 8

Step1: Identify points

Points: $(0,0), (3,1)$

Step2: Calculate slope

$m=\frac{1-0}{3-0}=\frac{1}{3}$
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Problem 9

Step1: Identify points

Points: $(0,1), (1,-2)$

Step2: Calculate slope

$m=\frac{-2-1}{1-0}=\frac{-3}{1}=-3$
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Problem 10

Part A: Paolo's slope

Step1: Define rate as slope

Rate = $\$15$ per photo, so $m=15$

Part B: Clear Image slope

Step1: Pick points from graph

Points: $(1,12), (4,48)$

Step2: Calculate slope

$m=\frac{48-12}{4-1}=\frac{36}{3}=12$

Part C: Compare slopes

$15>12$, so Paolo's Portraits is greater
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Problem 11

Part A: Henderson slope

Step1: Pick points from table

Points: $(10,3), (20,6)$

Step2: Calculate slope

$m=\frac{6-3}{20-10}=\frac{3}{10}=0.3$

Part B: Clarkson slope

Step1: Pick points from graph

Points: $(5,3.25), (10,4.50)$

Step2: Calculate slope

$m=\frac{4.50-3.25}{10-5}=\frac{1.25}{5}=0.25$

Part C: Compare slopes

$0.3>0.25$, so Henderson Toll Road is greater

Answer:

1. $-3$
2. $\frac{4}{5}$
3. $0$
4. $-7$
5. $-1$
6. $2$
7. $2$
8. $\frac{1}{3}$
9. $-3$
10. A. $15$; B. $12$; C. Paolo's Portraits
11. A. $0.3$; B. $0.25$; C. Henderson Toll Road