Worksheet displaying four coordinate planes with lines and point pairs, showing slope calculations for each line.

It looks like you've uploaded a worksheet titled "Calculate Slope from Points" with an answer key, and it's focused on finding the slope of a line given two points on a coordinate plane. Let's go through each problem step-by-step to understand how the slope is calculated and verify the answers.

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🔷 What is Slope?

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

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

This is often referred to as "rise over run".

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Let’s analyze each of the four problems shown in the image.

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🟦 Problem 1: Top Left Graph

- Points: $(-6, 6)$ and $(0, -6)$
- Using the formula:
$$
m = \frac{-6 - 6}{0 - (-6)} = \frac{-12}{6} = -2
$$
- ✔ Answer provided: -2 → Correct.

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🟨 Problem 2: Top Right Graph

- Points: $(-4, -4)$ and $(2, 3)$
- Calculate:
$$
m = \frac{3 - (-4)}{2 - (-4)} = \frac{3 + 4}{2 + 4} = \frac{7}{6}
$$
- ✔ Answer provided: $\frac{7}{6}$ → Correct.

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🟩 Problem 3: Bottom Left Graph

- Points: $(-5, -2)$ and $(5, -4)$
- Calculate:
$$
m = \frac{-4 - (-2)}{5 - (-5)} = \frac{-4 + 2}{5 + 5} = \frac{-2}{10} = -\frac{1}{5}
$$
- ✔ Answer provided: $-\frac{1}{5}$ → Correct.

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🟪 Problem 4: Bottom Right Graph

- Points: $(-2, 4)$ and $(2, -3)$
- Calculate:
$$
m = \frac{-3 - 4}{2 - (-2)} = \frac{-7}{4} = -\frac{7}{4}
$$
- ✔ Answer provided: $-\frac{7}{4}$ → Correct.

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✔ Final Check

All four slopes have been correctly calculated:

| Problem | Points | Slope Calculation | Answer |
|--------|--------------------|--------------------------|--------|
| 1 | (-6,6), (0,-6) | $ \frac{-12}{6} = -2 $ | -2 ✔ |
| 2 | (-4,-4), (2,3) | $ \frac{7}{6} $ | $ \frac{7}{6} $ ✔ |
| 3 | (-5,-2), (5,-4) | $ \frac{-2}{10} = -\frac{1}{5} $ | $ -\frac{1}{5} $ ✔ |
| 4 | (-2,4), (2,-3) | $ \frac{-7}{4} $ | $ -\frac{7}{4} $ ✔ |

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💡 Summary

Each problem uses the slope formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$
You identify two points from the graph, plug them into the formula, simplify the fraction, and get the slope.

✔ The answer key is correct for all four problems.

Let me know if you'd like a printable version or help with similar problems!