Worksheet for graphing linear equations using the slope-intercept method.

Let's solve each of the six linear equations using the slope-intercept method. The slope-intercept form is:

$$
y = mx + b
$$

Where:
- $ m $ is the slope
- $ b $ is the y-intercept

We'll follow these steps for each equation:

1. Identify the y-intercept ($ b $) — this is the point $ (0, b) $
2. Use the slope ($ m $) to find another point: rise over run
3. Draw a line through the points with arrows on both ends.

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1. $ y = -x + 5 $

- Slope ($ m $): $ -1 $ → rise = -1, run = 1
- Y-intercept ($ b $): $ 5 $ → point: $ (0, 5) $

Step-by-step:
- Plot $ (0, 5) $
- From there, go down 1 unit and right 1 unit → $ (1, 4) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, 5) $ and $ (1, 4) $, extending in both directions.

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2. $ y = -3x - 1 $

- Slope ($ m $): $ -3 $ → rise = -3, run = 1
- Y-intercept ($ b $): $ -1 $ → point: $ (0, -1) $

Step-by-step:
- Plot $ (0, -1) $
- From there, go down 3 units and right 1 unit → $ (1, -4) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, -1) $ and $ (1, -4) $

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3. $ y = \frac{2}{5}x + 2 $

- Slope ($ m $): $ \frac{2}{5} $ → rise = 2, run = 5
- Y-intercept ($ b $): $ 2 $ → point: $ (0, 2) $

Step-by-step:
- Plot $ (0, 2) $
- From there, go up 2 units and right 5 units → $ (5, 4) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, 2) $ and $ (5, 4) $

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4. $ y = -\frac{1}{6}x + 3 $

- Slope ($ m $): $ -\frac{1}{6} $ → rise = -1, run = 6
- Y-intercept ($ b $): $ 3 $ → point: $ (0, 3) $

Step-by-step:
- Plot $ (0, 3) $
- From there, go down 1 unit and right 6 units → $ (6, 2) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, 3) $ and $ (6, 2) $

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5. $ y = 2x + 6 $

- Slope ($ m $): $ 2 $ → rise = 2, run = 1
- Y-intercept ($ b $): $ 6 $ → point: $ (0, 6) $

Step-by-step:
- Plot $ (0, 6) $
- From there, go up 2 units and right 1 unit → $ (1, 8) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, 6) $ and $ (1, 8) $

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6. $ y = -\frac{3}{2}x - 5 $

- Slope ($ m $): $ -\frac{3}{2} $ → rise = -3, run = 2
- Y-intercept ($ b $): $ -5 $ → point: $ (0, -5) $

Step-by-step:
- Plot $ (0, -5) $
- From there, go down 3 units and right 2 units → $ (2, -8) $
- Draw a line through these points.

✔ Graph: Line passing through $ (0, -5) $ and $ (2, -8) $

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✔ Summary of Steps for Each Equation:

| Equation | Y-intercept | Slope | Direction |
|--------|-------------|-------|----------|
| 1. $ y = -x + 5 $ | $ (0, 5) $ | $ -1 $ | Down 1, Right 1 |
| 2. $ y = -3x - 1 $ | $ (0, -1) $ | $ -3 $ | Down 3, Right 1 |
| 3. $ y = \frac{2}{5}x + 2 $ | $ (0, 2) $ | $ \frac{2}{5} $ | Up 2, Right 5 |
| 4. $ y = -\frac{1}{6}x + 3 $ | $ (0, 3) $ | $ -\frac{1}{6} $ | Down 1, Right 6 |
| 5. $ y = 2x + 6 $ | $ (0, 6) $ | $ 2 $ | Up 2, Right 1 |
| 6. $ y = -\frac{3}{2}x - 5 $ | $ (0, -5) $ | $ -\frac{3}{2} $ | Down 3, Right 2 |

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🔍 How to Graph on Grids:

For each blank grid:
1. Mark the y-intercept on the y-axis.
2. Use the slope to plot one more point.
3. Connect the two points with a straight line.
4. Add arrows at both ends to show the line continues infinitely.

> 💡 Tip: If the slope is negative, the line goes downhill from left to right.

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If you're drawing this by hand:
- Use a ruler to draw straight lines.
- Label the axes if needed.
- Make sure your scale is consistent.

Let me know if you'd like a visual sketch or help plotting coordinates!