Graphing Linear Equations worksheet with four equations to graph on coordinate planes.

You're working on Graphing Linear Equations (A) — a worksheet that asks you to graph four linear equations using their slope-intercept form:
> y = mx + b
where:
- m is the slope (rise over run)
- b is the y-intercept (where the line crosses the y-axis)

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Let’s go through each equation one by one and explain how to graph it.

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🔹 Equation 1: `y = ½x - 3`

- Slope (m): ½ → rise 1, run 2 (up 1, right 2)
- Y-intercept (b): -3 → point (0, -3)

✔ Steps to graph:
1. Plot the y-intercept: (0, -3)
2. From there, use the slope: go up 1 unit, then right 2 units → new point: (2, -2)
3. Draw a straight line through these two points.

📌 *Optional*: You can also go down 1, left 2 from (0, -3) to get (-2, -4) for another point.

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🔹 Equation 2: `y = -¼x - 4`

- Slope (m): -¼ → rise -1, run 4 (down 1, right 4)
- Y-intercept (b): -4 → point (0, -4)

✔ Steps to graph:
1. Plot the y-intercept: (0, -4)
2. Use slope: go down 1, right 4 → new point: (4, -5)
3. Draw a straight line through these points.

📌 *Optional*: Go up 1, left 4 from (0, -4) → (-4, -3)

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🔹 Equation 3: `y = ⅔x + 9`

- Slope (m): ⅔ → rise 2, run 3 (up 2, right 3)
- Y-intercept (b): 9 → point (0, 9)

✔ Steps to graph:
1. Plot the y-intercept: (0, 9)
2. Use slope: go up 2, right 3 → new point: (3, 11)
3. Draw a straight line through these points.

📌 Since 9 is high on the grid, you may want to find a lower point:
- From (0, 9), go down 2, left 3 → (-3, 7)

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🔹 Equation 4: `y = -¾x + 8`

- Slope (m): -¾ → rise -3, run 4 (down 3, right 4)
- Y-intercept (b): 8 → point (0, 8)

✔ Steps to graph:
1. Plot the y-intercept: (0, 8)
2. Use slope: go down 3, right 4 → new point: (4, 5)
3. Draw a straight line through these points.

📌 Optional point: from (0, 8), go up 3, left 4 → (-4, 11)

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## ✔ Summary of Key Points for Each Graph:

| Equation | Y-Intercept | Slope | Two Points to Plot |
|----------------|-------------|-----------|----------------------------------|
| y = ½x - 3 | (0, -3) | ½ | (0, -3), (2, -2) |
| y = -¼x - 4 | (0, -4) | -¼ | (0, -4), (4, -5) |
| y = ⅔x + 9 | (0, 9) | ⅔ | (0, 9), (3, 11) or (-3, 7) |
| y = -¾x + 8 | (0, 8) | -¾ | (0, 8), (4, 5) or (-4, 11) |

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## 📌 Tips for Accurate Graphing:

- Always start with the y-intercept.
- Use the slope as a fraction: numerator = vertical change (rise), denominator = horizontal change (run).
- If slope is negative, go down for rise.
- Plot at least two points to ensure accuracy.
- Use a ruler to draw straight lines.

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✔ Once you’ve plotted each line correctly, your worksheet will be complete!

Let me know if you’d like me to generate printable graphs or visual sketches for each!