Worksheet for calculating the slope of lines using rise and run on coordinate planes.

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

Slope = rise / run

Where:
- Rise is how much the line goes up or down (change in y)
- Run is how much the line goes left or right (change in x)

We pick two points on the line, then calculate:

> Slope = (y₂ - y₁) / (x₂ - x₁)

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Problem 1)

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

Rise = -2 - 2 = -4
Run = -1 - (-3) = +2

Slope = -4 / 2 = -2

✔ Check: Line goes down as it moves right → negative slope. Makes sense.

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Problem 2)

Points: (-3, 1) and (1, 4)

Rise = 4 - 1 = +3
Run = 1 - (-3) = +4

Slope = 3 / 4

✔ Check: Line goes up slowly → positive fraction. Correct.

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Problem 3)

Points: (-4, 2) and (4, 0)

Rise = 0 - 2 = -2
Run = 4 - (-4) = +8

Slope = -2 / 8 = -1/4

✔ Simplified: Yes, -2÷2= -1, 8÷2=4 → -1/4

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Problem 4)

Points: (-4, -4) and (1, 1)

Rise = 1 - (-4) = +5
Run = 1 - (-4) = +5

Slope = 5 / 5 = 1

✔ Check: Diagonal going up at 45°? Yep, slope = 1.

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Problem 5)

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

Rise = -3 - (-3) = 0
Run = 2 - (-3) = +5

Slope = 0 / 5 = 0

✔ Horizontal line → always slope 0. Correct.

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Problem 6)

Points: (-4, -3) and (-2, 3)

Rise = 3 - (-3) = +6
Run = -2 - (-4) = +2

Slope = 6 / 2 = 3

✔ Steep upward line → large positive slope. Makes sense.

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Final Answer:
1) -2
2) 3/4
3) -1/4
4) 1
5) 0
6) 3