Finding slope from a graph worksheet with four example lines.

It looks like you've uploaded an image containing a math worksheet titled "Finding Slope from a Graph", with several graphs of lines on coordinate grids. The task is to find the slope of each line shown in the graphs.

Since I can't view images directly, I'll guide you through how to solve this type of problem step-by-step, and then you can apply it to your specific graphs.

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🔍 How to Find the Slope from a Graph

The slope of a line is a measure of how steep it is. It's 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 can pick any two points on the line, and use them to calculate the slope.

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✔ Step-by-Step Instructions:

1. Identify two points on the line that lie exactly on the grid intersections (so coordinates are easy to read).
2. Label the coordinates: Let’s say point A is $ (x_1, y_1) $ and point B is $ (x_2, y_2) $.
3. Calculate rise: $ y_2 - y_1 $
4. Calculate run: $ x_2 - x_1 $
5. Divide rise by run to get the slope.

> 💡 Remember:
> - If the line goes up as you move right → positive slope
> - If the line goes down as you move right → negative slope
> - Horizontal line → slope = 0
> - Vertical line → undefined slope

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📌 Example:

Suppose a line passes through points $ (1, 2) $ and $ (3, 6) $.

- Rise = $ 6 - 2 = 4 $
- Run = $ 3 - 1 = 2 $
- Slope = $ \frac{4}{2} = 2 $

So the slope is 2.

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Now, let's go through each graph (assuming there are 8 labeled graphs, A–H):

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🧩 Apply This to Each Graph:

Let’s assume the graphs look like this (based on common patterns):

#### Graph A: Line going up from left to right
- Pick two points: say $ (-2, -2) $ and $ (2, 2) $
- Rise = $ 2 - (-2) = 4 $
- Run = $ 2 - (-2) = 4 $
- Slope = $ \frac{4}{4} = 1 $

✔ Slope = 1

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#### Graph B: Line going down from left to right
- 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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#### Graph C: Steeper upward line
- Points: $ (-1, -3) $ and $ (1, 3) $
- Rise = $ 3 - (-3) = 6 $
- Run = $ 1 - (-1) = 2 $
- Slope = $ \frac{6}{2} = 3 $

✔ Slope = 3

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#### Graph D: Steeper downward line
- Points: $ (-1, 3) $ and $ (1, -3) $
- Rise = $ -3 - 3 = -6 $
- Run = $ 1 - (-1) = 2 $
- Slope = $ \frac{-6}{2} = -3 $

✔ Slope = -3

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#### Graph E: Gentle upward line
- Points: $ (0, 0) $ and $ (4, 2) $
- Rise = $ 2 - 0 = 2 $
- Run = $ 4 - 0 = 4 $
- Slope = $ \frac{2}{4} = \frac{1}{2} $

✔ Slope = ½

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#### Graph F: Gentle downward line
- Points: $ (0, 0) $ and $ (4, -2) $
- Rise = $ -2 - 0 = -2 $
- Run = $ 4 - 0 = 4 $
- Slope = $ \frac{-2}{4} = -\frac{1}{2} $

✔ Slope = -½

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#### Graph G: Vertical line
- All points have same $ x $-value (e.g., $ x = 2 $)
- Run = 0 → division by zero → undefined

✔ Slope = undefined

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#### Graph H: Horizontal line
- All points have same $ y $-value (e.g., $ y = 3 $)
- Rise = 0 → slope = 0

✔ Slope = 0

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✔ Final Answers (Example):

| Graph | Slope |
|-------|-----------|
| A | 1 |
| B | -1 |
| C | 3 |
| D | -3 |
| E | ½ |
| F | -½ |
| G | undefined |
| H | 0 |

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📌 Note: These answers are based on typical patterns seen in such worksheets. To be sure, please check the actual coordinates of the points on your graph.

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✔ Tips for Accuracy:

- Use grid lines to count squares carefully.
- Always go from left to right to avoid sign errors.
- Double-check if the line is vertical or horizontal.

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If you can describe the exact points or directions of the lines in your graphs, I can give you exact slopes for your specific case!