Graphing Lines in Slope Intercept Form Worksheet - Free Printable

You’ve uploaded a worksheet titled “Graphing Lines in Slope-Intercept Form” from Kuta Software – Infinite Pre-Algebra. The task is to sketch the graph of each line given its equation.

The slope-intercept form of a line is:

> y = mx + b

Where:
- m = slope (rise over run)
- b = y-intercept (where the line crosses the y-axis)

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Let’s solve each problem one by one, explaining how to graph it.

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1) y = –8x – 4

- Slope (m): –8 → This means for every 1 unit right, go down 8 units.
- Y-intercept (b): –4 → Start at point (0, –4)

✔ How to graph:
1. Plot the y-intercept: (0, –4)
2. From there, use slope –8/1 → move 1 right, 8 down → next point: (1, –12)
- Since the grid only goes to y = –6, you can also go *up* 8 and *left* 1: from (0, –4), go left 1, up 8 → (–1, 4)
3. Draw a straight line through these points.

📌 *Note: This line is very steep and negative.*

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2) y = –x + 5

- Slope (m): –1 → Down 1, right 1
- Y-intercept (b): 5 → Start at (0, 5)

✔ How to graph:
1. Plot (0, 5)
2. From there, go 1 right, 1 down → (1, 4)
3. Go another 1 right, 1 down → (2, 3)
4. Draw line through these points.

📌 *This is a diagonal line going down to the right.*

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3) y = 2x

- Slope (m): 2 → Up 2, right 1
- Y-intercept (b): 0 → Line passes through origin (0, 0)

✔ How to graph:
1. Plot (0, 0)
2. From there, go 1 right, 2 up → (1, 2)
3. Go another 1 right, 2 up → (2, 4)
4. Also go left 1, down 2 → (–1, –2)
5. Draw line through these points.

📌 *This line goes through the origin and rises steeply to the right.*

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4) x = –4

⚠️ Important: This is NOT in slope-intercept form — it’s a vertical line.

- All points have x = –4, regardless of y.
- It’s vertical and passes through x = –4 on the x-axis.

✔ How to graph:
1. Find x = –4 on the x-axis.
2. Draw a vertical line straight up and down through that point.
3. It will pass through (–4, 0), (–4, 1), (–4, –1), etc.

📌 *Vertical lines have undefined slope and cannot be written as y = mx + b.*

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5) y = (3/2)x + 3

- Slope (m): 3/2 → Up 3, right 2
- Y-intercept (b): 3 → Start at (0, 3)

✔ How to graph:
1. Plot (0, 3)
2. From there, go 2 right, 3 up → (2, 6) — but grid only goes to y=6, so that’s fine.
3. Go 2 left, 3 down → (–2, 0)
4. Draw line through (0,3), (2,6), and (–2,0)

📌 *This line rises gently to the right.*

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6) y = (1/5)x – 4

- Slope (m): 1/5 → Up 1, right 5
- Y-intercept (b): –4 → Start at (0, –4)

✔ How to graph:
1. Plot (0, –4)
2. From there, go 5 right, 1 up → (5, –3)
3. Go 5 left, 1 down → (–5, –5)
4. Draw line through these points.

📌 *This line is very shallow — rises slowly to the right.*

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## ✔ Final Tips for Graphing:

- Always start with the y-intercept (b).
- Use the slope (m) to find a second point.
- For fractions like 1/5 or 3/2, think “rise over run” — rise vertically, run horizontally.
- For vertical lines like x = –4, just draw a straight vertical line at that x-value.
- Connect the dots with a straight line using a ruler if possible.

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If you’d like me to generate actual images of the graphs or provide printable answer keys, let me know! But for now, you can sketch them on your worksheet using the steps above.

✔ You’re all set to complete this worksheet accurately!