Graphing lines in slope-intercept form worksheet with six equations and blank coordinate planes.

Let's solve each of these problems step by step. The goal is to graph each line given in slope-intercept form, which is:

$$
y = mx + b
$$

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

We'll use this information to sketch each line on the coordinate plane.

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1) $ y = \frac{1}{4}x - 1 $

- Slope ($ m $): $ \frac{1}{4} $
- Y-intercept ($ b $): $ -1 $

Steps:
1. Start at the y-intercept: $ (0, -1) $
2. Use slope $ \frac{1}{4} $: go up 1 unit, right 4 units to get next point: $ (4, 0) $
3. Draw a straight line through these points.

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

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2) $ y = -x + 2 $

- Slope ($ m $): $ -1 $
- Y-intercept ($ b $): $ 2 $

Steps:
1. Start at $ (0, 2) $
2. Slope $ -1 $: down 1, right 1 → $ (1, 1) $
3. Or up 1, left 1 → $ (-1, 3) $
4. Connect the dots.

✔ Graph: Line goes through $ (0, 2) $, $ (1, 1) $, $ (2, 0) $, etc.

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3) $ y = x + 1 $

- Slope ($ m $): $ 1 $
- Y-intercept ($ b $): $ 1 $

Steps:
1. Start at $ (0, 1) $
2. Slope $ 1 $: up 1, right 1 → $ (1, 2) $
3. Continue: $ (2, 3) $, $ (-1, 0) $, etc.

✔ Graph: Line through $ (0, 1) $, $ (1, 2) $, $ (-1, 0) $

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4) $ y = \frac{4}{3}x - 4 $

- Slope ($ m $): $ \frac{4}{3} $
- Y-intercept ($ b $): $ -4 $

Steps:
1. Start at $ (0, -4) $
2. Slope $ \frac{4}{3} $: up 4, right 3 → $ (3, 0) $
3. Next: $ (6, 4) $, or $ (-3, -8) $

✔ Graph: Line through $ (0, -4) $ and $ (3, 0) $

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5) $ y = -3x - 3 $

- Slope ($ m $): $ -3 $
- Y-intercept ($ b $): $ -3 $

Steps:
1. Start at $ (0, -3) $
2. Slope $ -3 $: down 3, right 1 → $ (1, -6) $
3. Or up 3, left 1 → $ (-1, 0) $

✔ Graph: Line through $ (0, -3) $, $ (1, -6) $, $ (-1, 0) $

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6) $ y = 4 $

This is a horizontal line.

- No $ x $ term → slope = 0
- Y-value is always 4

Steps:
1. Draw a horizontal line passing through $ y = 4 $
2. Every point has $ y = 4 $: e.g., $ (-5, 4), (0, 4), (5, 4) $

✔ Graph: Horizontal line at $ y = 4 $

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✔ Summary of Key Points for Each Graph:

| Equation | Slope | Y-intercept | Notes |
|--------|-------|-------------|-------|
| 1) $ y = \frac{1}{4}x - 1 $ | $ \frac{1}{4} $ | $ -1 $ | Rise 1, run 4 |
| 2) $ y = -x + 2 $ | $ -1 $ | $ 2 $ | Down 1, right 1 |
| 3) $ y = x + 1 $ | $ 1 $ | $ 1 $ | Up 1, right 1 |
| 4) $ y = \frac{4}{3}x - 4 $ | $ \frac{4}{3} $ | $ -4 $ | Rise 4, run 3 |
| 5) $ y = -3x - 3 $ | $ -3 $ | $ -3 $ | Down 3, right 1 |
| 6) $ y = 4 $ | $ 0 $ | $ 4 $ | Horizontal line |

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📌 How to Sketch:

For each graph:
1. Plot the y-intercept.
2. Use the slope to find another point.
3. Draw a straight line through both points.
4. Extend the line with arrows on both ends.

> Since you can't draw here, I recommend:
> - Mark the y-intercept first.
> - Use rise/run to plot a second point.
> - Draw a straight line through them.

Let me know if you'd like a visual description or help plotting specific points!