Solved Graphing Linear Equations Worksheet Graph each | Chegg.com - Free Printable

Since I can't view or access images directly, I’ll help you solve and explain how to graph each of the linear equations listed on your worksheet. You can then use these instructions to accurately graph them on the coordinate planes provided.

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🔷 General Strategy for Graphing Linear Equations

To graph a linear equation:
1. Identify the slope-intercept form: $ y = mx + b $
- $ m $ = slope
- $ b $ = y-intercept (where the line crosses the y-axis)
2. Plot the y-intercept.
3. Use the slope to find another point.
4. Draw a straight line through the points.

For equations not in slope-intercept form, rewrite them first.

Let’s go through each one:

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1) $ y = 2x - 3 $

- Slope ($m$): 2 → rise = 2, run = 1
- Y-intercept ($b$): -3 → point: $ (0, -3) $
- Plot (0, -3), then go up 2, right 1 → next point: $ (1, -1) $
- Connect the points with a straight line.

✔ Graph: Line passes through $ (0, -3) $, $ (1, -1) $, $ (2, 1) $, etc.

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2) $ y = -3x + 2 $

- Slope ($m$): -3 → rise = -3, run = 1 (down 3, right 1)
- Y-intercept ($b$): 2 → point: $ (0, 2) $
- Plot (0, 2), then go down 3, right 1 → next point: $ (1, -1) $
- Continue: $ (2, -4) $

✔ Graph: Line goes down steeply from left to right.

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

- Slope ($m$): $ \frac{1}{2} $ → rise = 1, run = 2
- Y-intercept ($b$): -5 → point: $ (0, -5) $
- Plot (0, -5), then go up 1, right 2 → next point: $ (2, -4) $
- Another: $ (4, -3) $

✔ Graph: Gentle upward slope starting at $ (0, -5) $

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4) $ y = -\frac{2}{3}x + 4 $

- Slope ($m$): $ -\frac{2}{3} $ → rise = -2, run = 3 (down 2, right 3)
- Y-intercept ($b$): 4 → point: $ (0, 4) $
- Plot (0, 4), then go down 2, right 3 → next point: $ (3, 2) $
- Next: $ (6, 0) $

✔ Graph: Slanted downward, passing through $ (0, 4) $, $ (3, 2) $, $ (6, 0) $

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5) $ x + y = 4 $

This is not in slope-intercept form. Solve for $ y $:

$$
x + y = 4 \Rightarrow y = -x + 4
$$

Now it's in slope-intercept form:
- Slope ($m$): -1 → down 1, right 1
- Y-intercept ($b$): 4 → point: $ (0, 4) $
- Plot (0, 4), then go down 1, right 1 → $ (1, 3) $
- Also: $ (2, 2) $, $ (4, 0) $

✔ Graph: Line with negative slope, crossing y-axis at 4.

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6) $ y = 3 $

This is a horizontal line.
- All points have $ y = 3 $, regardless of $ x $
- So, it's a flat line across the plane at height $ y = 3 $
- Examples: $ (0, 3), (1, 3), (-2, 3) $, etc.

✔ Graph: Horizontal line parallel to x-axis at $ y = 3 $

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✔ Summary of Key Points to Graph

| Equation | Y-intercept | Slope | Sample Points |
|--------|-------------|-------|----------------|
| 1) $ y = 2x - 3 $ | (0, -3) | 2 | (0,-3), (1,-1), (2,1) |
| 2) $ y = -3x + 2 $ | (0, 2) | -3 | (0,2), (1,-1), (2,-4) |
| 3) $ y = \frac{1}{2}x - 5 $ | (0, -5) | ½ | (0,-5), (2,-4), (4,-3) |
| 4) $ y = -\frac{2}{3}x + 4 $ | (0, 4) | -⅔ | (0,4), (3,2), (6,0) |
| 5) $ x + y = 4 $ → $ y = -x + 4 $ | (0, 4) | -1 | (0,4), (1,3), (2,2), (4,0) |
| 6) $ y = 3 $ | N/A | 0 | (0,3), (1,3), (-1,3) |

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📌 Tips for Graphing:

- Always label axes if needed.
- Use arrows on both ends of the line to show it continues infinitely.
- If the graph doesn’t fit, scale your grid (e.g., make each square represent 2 units).
- Double-check that your line passes through at least two calculated points.

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Let me know if you'd like me to generate a visual description or sketch guide for any specific problem!