Pre-Algebra Worksheets | Linear Functions Worksheets - Free Printable

Let’s solve each problem step by step. We’ll find the slope of each line using the formula:

Slope = (change in y) / (change in x) = rise / run

We pick two points on the line that are easy to read from the grid, then calculate how much we go up or down (rise) and how much we go left or right (run).

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Problem 1:

Pick two points: Let’s use (-4, 0) and (4, 2)

Rise = 2 - 0 = 2
Run = 4 - (-4) = 8
Slope = 2/8 = 1/4

✔ Check: From (-4,0), go up 1, right 4 → lands on (0,1). Go up 1 more, right 4 → (4,2). Yes! Slope is 1/4.

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Problem 2:

Pick two points: (-5, -2) and (5, -1)

Rise = -1 - (-2) = 1
Run = 5 - (-5) = 10
Slope = 1/10

✔ Check: Very flat line — makes sense for small slope like 1/10.

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Problem 3:

Pick two points: (1, 4) and (3, -2)

Rise = -2 - 4 = -6
Run = 3 - 1 = 2
Slope = -6/2 = -3

✔ Check: Steep downward line — negative slope, steepness matches -3.

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Problem 4:

Pick two points: (4, 5) and (5, -3)

Rise = -3 - 5 = -8
Run = 5 - 4 = 1
Slope = -8/1 = -8

✔ Check: Extremely steep downward — yes, slope of -8 fits.

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Problem 5:

Pick two points: (-5, 1) and (5, 3)

Rise = 3 - 1 = 2
Run = 5 - (-5) = 10
Slope = 2/10 = 1/5

✔ Check: Slight upward tilt — 1/5 is gentle, correct.

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Problem 6:

Pick two points: (-2, -5) and (1, 4)

Rise = 4 - (-5) = 9
Run = 1 - (-2) = 3
Slope = 9/3 = 3

✔ Check: Steep upward — slope of 3 is reasonable.

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Problem 7:

Pick two points: (-2, -4) and (2, 4)

Rise = 4 - (-4) = 8
Run = 2 - (-2) = 4
Slope = 8/4 = 2

✔ Check: Goes up 2 for every 1 right? From (-2,-4) to (0,0): up 4, right 2 → slope 2. Correct.

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Problem 8:

Pick two points: (-4, 2) and (4, -1)

Rise = -1 - 2 = -3
Run = 4 - (-4) = 8
Slope = -3/8

✔ Check: Gentle downward slope — -3/8 is about -0.375, which looks right on graph.

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Final Answer:
1) 1/4
2) 1/10
3) -3
4) -8
5) 1/5
6) 3
7) 2
8) -3/8