Practice worksheet for finding slope and y-intercept from linear graphs.

Let’s solve each problem one by one.

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Problem 1:

We need to find the slope and y-intercept from the graph.

- The line crosses the y-axis at (0, 3) → so y-intercept = 3
- To find slope: pick two points on the line. Let’s use (0, 3) and (-4, 0)
- Slope = rise / run = (change in y) / (change in x) = (0 - 3) / (-4 - 0) = (-3)/(-4) = 3/4
- Or from (0,3) to (4,6): (6-3)/(4-0) = 3/4 → same result.

✔ Slope = 3/4, y-intercept = 3

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Problem 2:

- Line crosses y-axis at (0, 2) → y-intercept = 2
- Pick two points: (0, 2) and (5, 0)
- Slope = (0 - 2)/(5 - 0) = -2/5

✔ Slope = -2/5, y-intercept = 2

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Problem 3:

- Line crosses y-axis at (0, -4) → y-intercept = -4
- Pick two points: (0, -4) and (2, 0)
- Slope = (0 - (-4)) / (2 - 0) = 4/2 = 2

✔ Slope = 2, y-intercept = -4

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Problem 4:

- Line crosses y-axis at (0, 1) → y-intercept = 1
- Pick two points: (0, 1) and (-2, 5)
- Slope = (5 - 1)/(-2 - 0) = 4 / (-2) = -2

✔ Slope = -2, y-intercept = 1

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Problem 5:

- Line crosses y-axis at (0, -1) → y-intercept = -1
- Pick two points: (0, -1) and (2, 2)
- Slope = (2 - (-1)) / (2 - 0) = 3/2

✔ Slope = 3/2, y-intercept = -1

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Problem 6:

- Line crosses y-axis at (0, 0) → y-intercept = 0
- Pick two points: (0, 0) and (2, 4)
- Slope = (4 - 0)/(2 - 0) = 4/2 = 2

✔ Slope = 2, y-intercept = 0

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Final Answer:
1. Slope: 3/4, y-intercept: 3
2. Slope: -2/5, y-intercept: 2
3. Slope: 2, y-intercept: -4
4. Slope: -2, y-intercept: 1
5. Slope: 3/2, y-intercept: -1
6. Slope: 2, y-intercept: 0