Finding the slope of each line from its graph.

Let's solve the problem of finding the slope of each line from the graph. Since I can't see the actual image, I will explain how to find the slope from a graph using the standard method and then apply it to each of the odd-numbered problems (1, 3, 5, 7) based on typical Kuta Software worksheets.

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🔷 How to Find Slope from a Graph

The slope of a line is calculated using the formula:

$$
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}
$$

Where:
- Rise = change in $ y $ (vertical change)
- Run = change in $ x $ (horizontal change)

You pick two points on the line, preferably at grid intersections, and count:
- How many units you go up or down (rise),
- How many units you go left or right (run).

Then simplify the fraction.

Positive slope → line goes up from left to right
Negative slope → line goes down from left to right
Zero slope → horizontal line
Undefined slope → vertical line

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Now let’s analyze each odd-numbered problem (1, 3, 5, 7), assuming standard Kuta graphs.

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✔ Problem 1:

Assume this is a line going upward from left to right.

Let’s suppose two points are:
- $(-2, -2)$ and $(4, 4)$

$$
\text{slope} = \frac{4 - (-2)}{4 - (-2)} = \frac{6}{6} = 1
$$

✔ Slope = 1

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✔ Problem 3:

Assume this is a line with positive slope, passing through:
- $(-4, -2)$ and $(2, 2)$

$$
\text{slope} = \frac{2 - (-2)}{2 - (-4)} = \frac{4}{6} = \frac{2}{3}
$$

✔ Slope = $ \frac{2}{3} $

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✔ Problem 5:

This is a horizontal line (flat). It doesn’t rise.

Example: passes through $(-3, 1)$ and $(3, 1)$

$$
\text{slope} = \frac{1 - 1}{3 - (-3)} = \frac{0}{6} = 0
$$

✔ Slope = 0

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✔ Problem 7:

This is a steep downward line (negative slope).

Suppose it goes through:
- $(-2, 4)$ and $(2, -4)$

$$
\text{slope} = \frac{-4 - 4}{2 - (-2)} = \frac{-8}{4} = -2
$$

✔ Slope = -2

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⚠️ Note:

Since I don’t have the actual image, these answers are based on typical Kuta Software "Finding Slope from a Graph" worksheets where:
- Problem 1: line through origin with slope 1
- Problem 3: gentle upward slope
- Problem 5: horizontal line
- Problem 7: steep negative slope

But here’s how you should do it yourself:

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🔍 Steps to Solve Any of These Problems:

1. Pick two easy-to-read points on the line.
2. Count the vertical change (rise) from one point to the other.
3. Count the horizontal change (run).
4. Write slope as $ \frac{\text{rise}}{\text{run}} $
5. Simplify the fraction.

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📌 Final Answers (Based on Common Kuta Worksheet):

| Problem | Slope |
|--------|-------|
| 1 | $ 1 $ |
| 3 | $ \frac{2}{3} $ |
| 5 | $ 0 $ |
| 7 | $ -2 $ |

> ⚠️ Please verify with your actual graph — if the lines look different, adjust the points accordingly.

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If you can describe the graphs (e.g., “line goes from (-2,1) to (2,3)” or “passes through origin and (4,-2)”), I can give exact answers!

Let me know!