Slope-intercept Form Worksheet Date Period - Free Printable

Let's solve each problem step by step.

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Part 1: Find the slope of each line (from graphs)

We'll use the slope formula:

$$
\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}
$$

We’ll identify two points on each line from the graph and compute the slope.

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#### 1) First Graph

From the graph:
- Line goes through points: $ (0, 3) $ and $ (2, -1) $

$$
m = \frac{-1 - 3}{2 - 0} = \frac{-4}{2} = -2
$$

✔ Slope = -2

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#### 2) Second Graph

Points: $ (-2, -2) $ and $ (2, 2) $

$$
m = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1
$$

✔ Slope = 1

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#### 3) Third Graph

This is a vertical line passing through $ x = -1 $. It goes through $ (-1, 3) $ and $ (-1, -1) $

Vertical lines have undefined slope because change in $ x = 0 $, so denominator is zero.

✔ Slope = undefined

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#### 4) Fourth Graph

Points: $ (1, 3) $ and $ (3, -1) $

$$
m = \frac{-1 - 3}{3 - 1} = \frac{-4}{2} = -2
$$

✔ Slope = -2

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#### 5) Fifth Graph

Horizontal line through $ y = -1 $. Points: $ (-2, -1) $, $ (0, -1) $, $ (2, -1) $

Change in $ y = 0 $, so slope = 0

✔ Slope = 0

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#### 6) Sixth Graph

Points: $ (-2, 3) $ and $ (2, -1) $

$$
m = \frac{-1 - 3}{2 - (-2)} = \frac{-4}{4} = -1
$$

✔ Slope = -1

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Part 2: Find the slope through each pair of points

Use the same formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

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#### 7) $(-14, -20), (-5, 9)$

$$
m = \frac{9 - (-20)}{-5 - (-14)} = \frac{9 + 20}{-5 + 14} = \frac{29}{9}
$$

✔ Slope = $ \frac{29}{9} $

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#### 8) $(-1, 1), (5, -6)$

$$
m = \frac{-6 - 1}{5 - (-1)} = \frac{-7}{6}
$$

✔ Slope = $ -\frac{7}{6} $

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#### 9) $(15, 9), (-14, -9)$

$$
m = \frac{-9 - 9}{-14 - 15} = \frac{-18}{-29} = \frac{18}{29}
$$

✔ Slope = $ \frac{18}{29} $

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#### 10) $(2, -12), (18, 15)$

$$
m = \frac{15 - (-12)}{18 - 2} = \frac{15 + 12}{16} = \frac{27}{16}
$$

✔ Slope = $ \frac{27}{16} $

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✔ Final Answers:

| Problem | Slope |
|--------|-------|
| 1) | $-2$ |
| 2) | $1$ |
| 3) | Undefined |
| 4) | $-2$ |
| 5) | $0$ |
| 6) | $-1$ |
| 7) | $\frac{29}{9}$ |
| 8) | $-\frac{7}{6}$ |
| 9) | $\frac{18}{29}$ |
| 10) | $\frac{27}{16}$ |

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Let me know if you'd like these explained further or want help with slope-intercept form next!