Lesson 11
FUSD AZCCRS- MATHEMATICS CURRICULUM
8•4
Lesson 11: The Slope of a Non-Vertical Line
Opening Exercise
Graph A
a.
Graph B
Which graph is steeper?
The slope of a line is found by writing the vertical rise over the horizontal run.
b.
What is the slope of each of the lines? Use the directions above to figure each one out.
2.
What is the slope of these non-vertical line? If the vertical rise goes down from the point on the left to the point on the right,
the slope is NEGATIVE.
S.30
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 11
FUSD AZCCRS- MATHEMATICS CURRICULUM
3.
What is the slope of this non-vertical line?
4.
Find the slope of the line below? How is this different from previous examples?
8•4
Exercises
5.
Find at least three solutions to the equation 𝑦 = 2𝑥, and graph the solutions as points on the coordinate plane. Connect the
points to make a line. Find the slope of the line.
x
y
S.31
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 11
FUSD AZCCRS- MATHEMATICS CURRICULUM
6.
8•4
Find at least three solutions to the equation 𝑦 = 3𝑥 − 1, and graph the solutions as points on the coordinate plane. Connect
the points to make a line. Find the slope of the line.
x
y
7.
The graph of the equation 𝑦 = 7𝑥 − 3 has what slope?
8.
The graph of the equation 𝑦 = − 𝑥 − 3 has what slope?
9.
You have $20 in savings at the bank. Each week, you add $2 to your savings. Let 𝑦 represent the total amount of money you
have saved at the end of 𝑥 weeks. Write an equation to represent this situation, and identify the slope of the equation. What
does that number represent?
3
4
10. A friend is training for a marathon. She can run 4 miles in 28 minutes. Assume she runs at a constant rate. Write an equation
to represent the total distance, 𝑦, your friend can run in 𝑥 minutes. Identify the slope of the equation. What does that number
represent?
S.32
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 11
FUSD AZCCRS- MATHEMATICS CURRICULUM
8•4
11. Four boxes of pencils cost $5. Write an equation that represents the total cost, 𝑦, for 𝑥 boxes of pencils. What is the slope of
the equation? What does that number represent?
12. Solve the following equation for 𝑦, and then identify the slope of the line: 9𝑥 − 3𝑦 = 15.
13. Solve the following equation for 𝑦, and then identify the slope of the line: 5𝑥 + 9𝑦 = 8.
14. Solve the following equation for 𝑦, and then identify the slope of the line: 𝑎𝑥 + 𝑏𝑦 = 𝑐.
S.33
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G8-M4-TE-1.3.0-09.2015
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.