Slope-intercept form worksheet for Algebra 1 students, including graph-based and point-based slope calculation exercises.

Let's solve this Slope-Intercept Form Worksheet step by step. We are asked to:

1. Find the slope of each line from the graphs (problems 1–6).
2. Find the slope of the line through each pair of points (problems 7–10).

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🔷 Slope Formula:

The slope $ m $ of a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

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

This is also known as rise over run.

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## ✔ Part 1: Find the slope of each line from the graph (1–6)

We’ll estimate coordinates from the graphs and calculate the slope.

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1)

From the graph:
- The line passes through points: $ (0, 3) $ and $ (2, -1) $

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

✔ Slope = -2

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2)

Points on the line: $ (0, -2) $ and $ (3, 1) $

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

✔ Slope = 1

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3)

Vertical line through $ x = -2 $. It goes through $ (-2, 3) $ and $ (-2, -2) $

For vertical lines, $ x $ doesn't change → undefined slope

✔ Slope = undefined

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4)

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

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

✔ Slope = -4

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5)

Horizontal line at $ y = 1 $. Points: $ (-1, 1) $ and $ (2, 1) $

No change in $ y $ → slope is zero.

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

✔ Slope = 0

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6)

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 (7–10)

Use the slope formula:

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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:

Graphs (1–6):

1) $ -2 $
2) $ 1 $
3) undefined
4) $ -4 $
5) $ 0 $
6) $ -1 $

Point Pairs (7–10):

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 answers formatted for a worksheet or need explanations for any specific problem!