Graphing Lines SI.ks-ia1 - Kuta Software - Free Printable

Let's solve each of these graphing problems step by step. The goal is to sketch the graph of each line given by its equation. We'll use the slope-intercept form $ y = mx + b $, where:

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

We'll also handle special cases like horizontal and vertical lines.

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1) $ y = \frac{7}{2}x - 2 $

- Slope (m): $ \frac{7}{2} = 3.5 $
- Y-intercept (b): $ -2 $

Steps:
1. Start at the y-intercept: $ (0, -2) $
2. Use slope $ \frac{7}{2} $: rise 7, run 2
- From $ (0, -2) $, go up 7 units and right 2 units → $ (2, 5) $
3. Plot both points and draw a line through them.

✔ Graph: A line passing through $ (0, -2) $ and $ (2, 5) $, rising steeply.

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2) $ y = -6x + 3 $

- Slope (m): $ -6 $
- Y-intercept (b): $ 3 $

Steps:
1. Start at $ (0, 3) $
2. Slope = $ -6 $ → down 6, right 1
- From $ (0, 3) $, go down 6 → $ (1, -3) $
3. Plot both points and draw the line.

✔ Graph: Steeply decreasing line through $ (0, 3) $ and $ (1, -3) $

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3) $ y = -5 $

This is a horizontal line.

- All points have $ y = -5 $, regardless of $ x $
- So it’s a flat line crossing the y-axis at $ -5 $

Example points: $ (-2, -5), (0, -5), (2, -5) $

✔ Graph: Horizontal line at $ y = -5 $

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4) $ y = \frac{6}{5}x + 1 $

- Slope (m): $ \frac{6}{5} = 1.2 $
- Y-intercept (b): $ 1 $

Steps:
1. Start at $ (0, 1) $
2. Rise 6, run 5 → from $ (0, 1) $, go up 6, right 5 → $ (5, 7) $
3. Plot both points and draw the line.

✔ Graph: Line through $ (0, 1) $ and $ (5, 7) $, moderately increasing

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5) $ y = -\frac{1}{4}x + 2 $

- Slope (m): $ -\frac{1}{4} $
- Y-intercept (b): $ 2 $

Steps:
1. Start at $ (0, 2) $
2. Slope = $ -\frac{1}{4} $ → down 1, right 4
- From $ (0, 2) $, go down 1, right 4 → $ (4, 1) $
3. Plot both points and draw the line.

✔ Graph: Gently decreasing line through $ (0, 2) $ and $ (4, 1) $

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6) $ x = 5 $

This is a vertical line.

- All points have $ x = 5 $, regardless of $ y $
- So it’s a vertical line passing through $ x = 5 $

Example points: $ (5, -2), (5, 0), (5, 3) $

✔ Graph: Vertical line at $ x = 5 $

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✔ Summary of How to Graph Each:

| Equation | Type | Key Points |
|--------|------|-----------|
| 1) $ y = \frac{7}{2}x - 2 $ | Linear (positive slope) | (0, -2), (2, 5) |
| 2) $ y = -6x + 3 $ | Linear (negative slope) | (0, 3), (1, -3) |
| 3) $ y = -5 $ | Horizontal line | Any point with $ y = -5 $ |
| 4) $ y = \frac{6}{5}x + 1 $ | Linear (positive slope) | (0, 1), (5, 7) |
| 5) $ y = -\frac{1}{4}x + 2 $ | Linear (negative slope) | (0, 2), (4, 1) |
| 6) $ x = 5 $ | Vertical line | Any point with $ x = 5 $ |

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📌 Final Answer:

To complete the worksheet:
- For each equation, plot the y-intercept first.
- Use the slope to find a second point.
- Draw a straight line through the two points.
- For $ y = -5 $, draw a horizontal line across $ y = -5 $.
- For $ x = 5 $, draw a vertical line across $ x = 5 $.

> 🔧 Tip: Use graph paper carefully. Label axes and scale appropriately (each square is usually 1 unit).

Let me know if you'd like me to generate the actual sketches or provide coordinates for plotting!