Students use this worksheet to calculate the slope of lines by identifying the rise and run on nine different coordinate grids.

Let's solve each problem step by step to find the slope of each line on the graph. The slope is calculated using the formula:

$$
\text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1}
$$

We'll identify two points on each line (usually marked with dots), calculate the rise (change in $ y $) and run (change in $ x $), then compute the slope.

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1)

Points: $(-2, -2)$ and $(2, 4)$
- Rise = $4 - (-2) = 6$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{6}{4} = \frac{3}{2} $

✔ Slope = $ \frac{3}{2} $

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2)

Points: $(-2, 4)$ and $(2, -2)$
- Rise = $-2 - 4 = -6$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{-6}{4} = -\frac{3}{2} $

✔ Slope = $ -\frac{3}{2} $

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3)

Points: $(-2, -2)$ and $(2, 4)$
- Rise = $4 - (-2) = 6$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{6}{4} = \frac{3}{2} $

✔ Slope = $ \frac{3}{2} $

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4)

Points: $(-2, 4)$ and $(2, -2)$
- Rise = $-2 - 4 = -6$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{-6}{4} = -\frac{3}{2} $

✔ Slope = $ -\frac{3}{2} $

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5)

Points: $(-2, -2)$ and $(2, 2)$
- Rise = $2 - (-2) = 4$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{4}{4} = 1 $

✔ Slope = $ 1 $

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6)

Points: $(-2, 2)$ and $(2, 0)$
- Rise = $0 - 2 = -2$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{-2}{4} = -\frac{1}{2} $

✔ Slope = $ -\frac{1}{2} $

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7)

Points: $(-2, -2)$ and $(2, 4)$
- Rise = $4 - (-2) = 6$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{6}{4} = \frac{3}{2} $

✔ Slope = $ \frac{3}{2} $

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8)

Points: $(-2, 2)$ and $(2, -2)$
- Rise = $-2 - 2 = -4$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{-4}{4} = -1 $

✔ Slope = $ -1 $

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9)

Points: $(-2, 1)$ and $(2, 2)$
- Rise = $2 - 1 = 1$
- Run = $2 - (-2) = 4$
- Slope = $ \frac{1}{4} $

✔ Slope = $ \frac{1}{4} $

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✔ Final Answers:

1) $ \frac{3}{2} $
2) $ -\frac{3}{2} $
3) $ \frac{3}{2} $
4) $ -\frac{3}{2} $
5) $ 1 $
6) $ -\frac{1}{2} $
7) $ \frac{3}{2} $
8) $ -1 $
9) $ \frac{1}{4} $

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Let me know if you'd like this as a printable answer sheet or need explanations for any specific graph!