Printable math worksheet for finding slope using the ratio method.

You've uploaded a worksheet titled “Finding Slope: Ratio method”. The goal is to find the slope of a line passing through two given points using the ratio method, which means calculating:

> Slope = Δy / Δx = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

The example at the top shows how to do it:
- Points: (4, 6) and (7, 1)
- Δy = 1 - 6 = -5
- Δx = 7 - 4 = 3
- Slope = -5/3

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Now, let’s solve each problem step by step.

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Problem 1: (5, -3) and (-1, 6)

Δy = 6 - (-3) = 6 + 3 = 9
Δx = -1 - 5 = -6
Slope = Δy / Δx = 9 / (-6) = -3/2

✔ Answer: Slope = -3/2

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Problem 2: (7, 2) and (4, 8)

Δy = 8 - 2 = 6
Δx = 4 - 7 = -3
Slope = 6 / (-3) = -2

✔ Answer: Slope = -2

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Problem 3: (1, 4) and (7, -2)

Δy = -2 - 4 = -6
Δx = 7 - 1 = 6
Slope = -6 / 6 = -1

✔ Answer: Slope = -1

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Problem 4: (-4, 4) and (2, 9)

Δy = 9 - 4 = 5
Δx = 2 - (-4) = 2 + 4 = 6
Slope = 5 / 6

✔ Answer: Slope = 5/6

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Problem 5: (-8, 2) and (3, 5)

Δy = 5 - 2 = 3
Δx = 3 - (-8) = 3 + 8 = 11
Slope = 3 / 11

✔ Answer: Slope = 3/11

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Problem 6: (-5, 3) and (1, 10)

Δy = 10 - 3 = 7
Δx = 1 - (-5) = 1 + 5 = 6
Slope = 7 / 6

✔ Answer: Slope = 7/6

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Problem 7: (-2, -3) and (-7, -1)

Δy = -1 - (-3) = -1 + 3 = 2
Δx = -7 - (-2) = -7 + 2 = -5
Slope = 2 / (-5) = -2/5

✔ Answer: Slope = -2/5

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Problem 8: (0, 1) and (4, 9)

Δy = 9 - 1 = 8
Δx = 4 - 0 = 4
Slope = 8 / 4 = 2

✔ Answer: Slope = 2

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## ✔ Final Answers Summary:

1. Slope = -3/2
2. Slope = -2
3. Slope = -1
4. Slope = 5/6
5. Slope = 3/11
6. Slope = 7/6
7. Slope = -2/5
8. Slope = 2

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## 💡 Explanation Recap:

- Slope measures how steep a line is.
- It’s calculated as rise over run: vertical change (Δy) divided by horizontal change (Δx).
- Always subtract the first point from the second point consistently: (y₂ - y₁) / (x₂ - x₁).
- Reduce fractions when possible.
- A positive slope means the line goes up from left to right; negative means it goes down.

Let me know if you’d like a visual graph or more practice! 📈