Worksheet titled "Finding Slope From a Graph" with six problems, each displaying a line on a grid to determine slope.

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

Slope = rise / run

- Rise is how much the line goes up (positive) or down (negative) between two points.
- Run is how much the line goes right (positive) or left (negative) between those same two points.

We can pick any two clear points on the line — preferably where the line crosses grid intersections — and count the vertical change (rise) and horizontal change (run).

Let’s go through each problem one by one.

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Problem 1:

Pick two points: Let’s use (-4, -2) and (0, 1).
From (-4, -2) to (0, 1):
→ Rise = 1 - (-2) = 3
→ Run = 0 - (-4) = 4
Slope = 3/4

✔ Check with another pair: Use (0,1) and (4,4)
Rise = 4 - 1 = 3
Run = 4 - 0 = 4 → Slope = 3/4 ✔️

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Problem 2:

Points: Let’s use (0, 2) and (4, -2)
Rise = -2 - 2 = -4
Run = 4 - 0 = 4
Slope = -4/4 = -1

✔ Check: Use (-2, 4) and (2, 0)
Rise = 0 - 4 = -4
Run = 2 - (-2) = 4 → Slope = -1 ✔️

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Problem 3:

Points: Use (-4, -3) and (0, -1)
Rise = -1 - (-3) = 2
Run = 0 - (-4) = 4
Slope = 2/4 = 1/2

✔ Check: Use (0,-1) and (4,1)
Rise = 1 - (-1) = 2
Run = 4 - 0 = 4 → Slope = 1/2 ✔️

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Problem 4:

Points: Use (0, 4) and (4, 0)
Rise = 0 - 4 = -4
Run = 4 - 0 = 4
Slope = -4/4 = -1

✔ Check: Use (-2, 6) and (2, 2)
Rise = 2 - 6 = -4
Run = 2 - (-2) = 4 → Slope = -1 ✔️

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Problem 5:

This is a horizontal line. All y-values are the same (y = -1).
No matter which two points you pick, rise = 0.
So slope = 0 / run = 0

✔ Example: Points (-3, -1) and (3, -1)
Rise = -1 - (-1) = 0
Run = 3 - (-3) = 6 → Slope = 0/6 = 0 ✔️

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Problem 6:

Points: Use (0, -3) and (1, 3)
Rise = 3 - (-3) = 6
Run = 1 - 0 = 1
Slope = 6/1 = 6

✔ Check: Use (-1, -9) and (0, -3)
Rise = -3 - (-9) = 6
Run = 0 - (-1) = 1 → Slope = 6 ✔️

*(Note: The line passes through (0,-3), (1,3), so yes, steep positive slope)*

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Problem 7:

Points: Use (0, 0) and (2, -4)
Rise = -4 - 0 = -4
Run = 2 - 0 = 2
Slope = -4/2 = -2

✔ Check: Use (-1, 2) and (1, -2)
Rise = -2 - 2 = -4
Run = 1 - (-1) = 2 → Slope = -2 ✔️

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Problem 8:

This is a vertical line. All x-values are the same (x = 0).
Run = 0 for any two points.
Division by zero is undefined → slope is undefined

✔ Example: Points (0, -3) and (0, 3)
Rise = 3 - (-3) = 6
Run = 0 - 0 = 0 → Slope = 6/0 → undefined ✔️

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Final Answer:

1. 3/4
2. -1
3. 1/2
4. -1
5. 0
6. 6
7. -2
8. undefined