Math worksheet for practicing finding the slope between two points using coordinate grids.

Let’s solve each problem step by step. We’re finding the slope between two points using the formula:

> Slope = (y₂ - y₁) / (x₂ - x₁)

We’ll go one by one, carefully subtracting and dividing.

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(1) Points: (-4, 3) and (2, 0)
→ y₂ - y₁ = 0 - 3 = -3
→ x₂ - x₁ = 2 - (-4) = 2 + 4 = 6
→ Slope = -3 / 6 = -1/2

✔ Check: Negative slope makes sense — going down from left to right.

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(2) Points: (-2, 4) and (2, -2)
→ y₂ - y₁ = -2 - 4 = -6
→ x₂ - x₁ = 2 - (-2) = 2 + 2 = 4
→ Slope = -6 / 4 = -3/2

✔ Simplified fraction.

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(3) Points: (-5, -2) and (3, 3)
→ y₂ - y₁ = 3 - (-2) = 3 + 2 = 5
→ x₂ - x₁ = 3 - (-5) = 3 + 5 = 8
→ Slope = 5 / 8

✔ Positive slope — goes up as we move right.

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(4) Points: (-2, 3) and (4, 3)
→ y₂ - y₁ = 3 - 3 = 0
→ x₂ - x₁ = 4 - (-2) = 6
→ Slope = 0 / 6 = 0

✔ Horizontal line → slope is zero.

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(5) Points: (0, -4) and (4, -2)
→ y₂ - y₁ = -2 - (-4) = -2 + 4 = 2
→ x₂ - x₁ = 4 - 0 = 4
→ Slope = 2 / 4 = 1/2

✔ Reduced fraction.

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(6) Points: (3, 0) and (2, 3)
→ y₂ - y₁ = 3 - 0 = 3
→ x₂ - x₁ = 2 - 3 = -1
→ Slope = 3 / (-1) = -3

✔ Steep negative slope.

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(7) Points: (-4, -3) and (2, 2)
→ y₂ - y₁ = 2 - (-3) = 2 + 3 = 5
→ x₂ - x₁ = 2 - (-4) = 6
→ Slope = 5 / 6

✔ Positive, less than 1.

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(8) Points: (0, 0) and (2, 2)
→ y₂ - y₁ = 2 - 0 = 2
→ x₂ - x₁ = 2 - 0 = 2
→ Slope = 2 / 2 = 1

✔ Diagonal line at 45° — slope = 1.

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(9) Points: (-3, 2) and (3, -1)
→ y₂ - y₁ = -1 - 2 = -3
→ x₂ - x₁ = 3 - (-3) = 6
→ Slope = -3 / 6 = -1/2

✔ Same as #1 — same steepness but different position.

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(10) Points: (-4, 0) and (2, 2)
→ y₂ - y₁ = 2 - 0 = 2
→ x₂ - x₁ = 2 - (-4) = 6
→ Slope = 2 / 6 = 1/3

✔ Gentle positive slope.

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(11) Points: (0, 4) and (3, 1)
→ y₂ - y₁ = 1 - 4 = -3
→ x₂ - x₁ = 3 - 0 = 3
→ Slope = -3 / 3 = -1

✔ Perfect diagonal downward.

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(12) Points: (-3, 0) and (3, -2)
→ y₂ - y₁ = -2 - 0 = -2
→ x₂ - x₁ = 3 - (-3) = 6
→ Slope = -2 / 6 = -1/3

✔ Gentle negative slope.

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Final Answer:
(1) -1/2
(2) -3/2
(3) 5/8
(4) 0
(5) 1/2
(6) -3
(7) 5/6
(8) 1
(9) -1/2
(10) 1/3
(11) -1
(12) -1/3