Slope and linear functions worksheet

Grade 8 math, Common Core 8.EE.B.6. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Slope and linear functions

Grade 8 math, Common Core 8.EE.B.6

Find the slope, or write the equation of the line.

1.
Find the slope of the line shown in the table.
x 0 1 2 3
y 9 7 5 3
2.
What are the slope and y-intercept of 4x + y = 12?
3.
Find the slope of the line through (−4, 3) and (−6, −2).
4.
Find the slope of the line shown in the table.
x 0 1 2 3
y 6 11 16 21
5.
Write the equation of the line with slope −3 and y-intercept 5.
6.
What are the slope and y-intercept of 3x + y = 3?
7.
Find the slope of the line shown in the table.
x 0 1 2 3
y 2 6 10 14
8.
Find the slope of the line through (−3, −6) and (−4, −8).
9.
Find the slope of the line through (2, −3) and (−3, 1).
10.
Find the slope of the line through (−2, 3) and (−5, −3).

x	0	1	2	3
y	9	7	5	3

x	0	1	2	3
y	6	11	16	21

x	0	1	2	3
y	2	6	10	14

Answer key: Slope and linear functions

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. −2
y changes by −2 each time x goes up by 1
2. Slope −4, y-intercept 12
y = −4x + 12
3. 52
(−2 − 3) ÷ (−6 − (−4)) = −5 ÷ (−2)= 52
4. 5
y changes by 5 each time x goes up by 1
5. y = −3x + 5
6. Slope −3, y-intercept 3
y = −3x + 3
7. 4
y changes by 4 each time x goes up by 1
8. 2
(−8 − (−6)) ÷ (−4 − (−3)) = −2 ÷ (−1)= 2
9. −45
(1 − (−3)) ÷ (−3 − 2) = 4 ÷ (−5)= −45
10. 2
(−3 − 3) ÷ (−5 − (−2)) = −6 ÷ (−3)= 2

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About slope and linear functions

Slope measures how steep a line is: the change in y divided by the change in x between any two points, often called rise over run. In y = mx + b, m is the slope and b is the y-intercept, where the line crosses the y-axis. A positive slope goes up from left to right; a negative slope goes down.

Worked example 1

Find the slope of the line through (−4, −5) and (−7, −14).

Step 1.(−14 − (−5)) ÷ (−7 − (−4)) = −9 ÷ (−3)
Step 2.= 3

Answer: 3

Worked example 2

What are the slope and y-intercept of −x + y = 5?

Step 1.y = x + 5

Answer: Slope 1, y-intercept 5

Example 3

Write the equation of the line with slope 12 and y-intercept −1.

Answer: y = 12x − 1

Watch out for

Subtract in the same order on top and bottom: (y₂ − y₁) ÷ (x₂ − x₁).
Get y alone before reading the slope: 2x + y = 7 becomes y = −2x + 7.
Simplify the slope as a fraction.

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