Graphing Linear Equations Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step and explain how to graph each linear equation on the coordinate plane.

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① y = -4

This is a horizontal line.
- For any value of x, y is always -4.
- So, you plot points like: (0, -4), (1, -4), (-2, -4), etc.
- Draw a straight horizontal line through y = -4.

✔ Graph: A horizontal line crossing the y-axis at -4.

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② y = 2x + 3

This is in slope-intercept form (y = mx + b), where:
- Slope (m) = 2
- y-intercept (b) = 3 → point (0, 3)

Steps to graph:
1. Plot the y-intercept: (0, 3)
2. Use slope = 2 = rise/run = 2/1 → from (0, 3), go up 2, right 1 → next point (1, 5)
3. Go down 2, left 1 → (−1, 1)
4. Draw a line through these points.

✔ Graph: Line passing through (0,3), (1,5), (−1,1), etc.

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③ x + y = 6

Rewrite in slope-intercept form:

> y = -x + 6

Now:
- Slope (m) = -1
- y-intercept (b) = 6 → point (0, 6)

Steps to graph:
1. Plot (0, 6)
2. Slope = -1 → go down 1, right 1 → (1, 5)
3. Or go up 1, left 1 → (−1, 7)
4. Draw the line.

✔ Graph: Line with negative slope, crossing y-axis at 6.

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④ y = (1/2)x - 5

Slope-intercept form:
- Slope (m) = 1/2
- y-intercept (b) = -5 → point (0, -5)

Steps to graph:
1. Plot (0, -5)
2. Slope = 1/2 → rise 1, run 2 → from (0, -5), go up 1, right 2 → (2, -4)
3. Also, go down 1, left 2 → (−2, -6)
4. Draw the line.

✔ Graph: Gentle upward-sloping line crossing y-axis at -5.

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⑤ x = 4

This is a vertical line.
- For any value of y, x is always 4.
- Points: (4, 0), (4, 3), (4, -2), etc.

✔ Graph: Vertical line crossing the x-axis at 4.

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⑥ y = (1/4)x + 3y

⚠️ This equation looks incorrect as written — it has y on both sides.

Let’s fix it algebraically:

> y = (1/4)x + 3y

Subtract 3y from both sides:

> y - 3y = (1/4)x
> -2y = (1/4)x

Divide both sides by -2:

> y = -(1/8)x

✔ So the corrected equation is: y = - (1/8)x

Now graph this:

- Slope (m) = -1/8
- y-intercept (b) = 0 → passes through origin (0, 0)

Steps to graph:
1. Plot (0, 0)
2. Slope = -1/8 → go down 1, right 8 → (8, -1)
3. Or up 1, left 8 → (-8, 1)
4. Draw the line.

✔ Graph: Very shallow downward-sloping line through the origin.

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## ✔ Final Answer Summary:

| Problem | Equation | Type | Key Points / Notes |
|---------|----------------------|----------------|---------------------------------------------|
| ① | y = -4 | Horizontal | All points have y = -4 |
| ② | y = 2x + 3 | Slanted | y-int (0,3), slope 2 |
| ③ | x + y = 6 → y = -x+6 | Slanted | y-int (0,6), slope -1 |
| ④ | y = (1/2)x - 5 | Slanted | y-int (0,-5), slope 1/2 |
| ⑤ | x = 4 | Vertical | All points have x = 4 |
| ⑥ | y = (1/4)x + 3y → y = -(1/8)x | Slanted (shallow) | Through origin, slope -1/8 |

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📌 Note for #6: The original equation was likely a typo. If it was meant to be y = (1/4)x + 3, then it would be a different graph (y-int = 3, slope = 1/4). But as written, we must solve it algebraically, which leads to y = -(1/8)x.

If you intended a different equation for #6, let me know — otherwise, this is the mathematically correct interpretation.

You can now graph each line on its respective grid using the instructions above! 📈