Worksheet for finding the slope of a line from a graph, featuring six different linear equations plotted on coordinate grids.

To find the slope (m) of a line from a graph, we use the formula:

> m = rise / run = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

We pick two clear points on the line (preferably where the line crosses grid intersections), then count how many units you go up/down (rise) and left/right (run) to get from one point to the other.

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Let’s solve each problem one by one.

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Problem 1

Line goes from top-left to bottom-right → negative slope.

Pick two points:
- Point A: (0, 2) — crosses y-axis at 2
- Point B: (2, -2) — go right 2, down 4

Rise = -2 - 2 = -4
Run = 2 - 0 = 2

→ m = -4 / 2 = -2

✔ Answer: m = -2

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Problem 2

Line is almost flat, slightly going down → small negative slope.

Pick two points:
- Point A: (-4, 2)
- Point B: (4, 0)

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

→ m = -2 / 8 = -1/4

✔ Answer: m = -1/4

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Problem 3

Line goes up to the right → positive slope, gentle incline.

Pick two points:
- Point A: (-4, 0)
- Point B: (4, 2)

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

→ m = 2 / 8 = 1/4

✔ Answer: m = 1/4

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Problem 4

Line goes up to the right → positive slope, steeper than #3.

Pick two points:
- Point A: (-4, -2)
- Point B: (0, 2)

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

→ m = 4 / 4 = 1

✔ Answer: m = 1

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Problem 5

Very steep line going up to the right → large positive slope.

Pick two points:
- Point A: (0, -2)
- Point B: (2, 6)

Rise = 6 - (-2) = 8
Run = 2 - 0 = 2

→ m = 8 / 2 = 4

✔ Answer: m = 4

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Problem 6

Line goes down to the right → negative slope, very gentle.

Pick two points:
- Point A: (-4, 1)
- Point B: (4, 0)

Rise = 0 - 1 = -1
Run = 4 - (-4) = 8

→ m = -1 / 8

✔ Answer: m = -1/8

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## ✔ Final Answers:

1. m = -2
2. m = -1/4
3. m = 1/4
4. m = 1
5. m = 4
6. m = -1/8

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💡 Tip:

Always double-check your points and direction:
- If line goes up as you go right → positive slope
- If line goes down as you go right → negative slope
- Steeper line = larger absolute value of slope
- Horizontal line → slope = 0
- Vertical line → undefined slope (not here)

Let me know if you want to see the graphs with points marked!