Worksheet for graphing linear equations on coordinate planes.

Let’s solve each equation step by step. We’ll find two points for each line (usually the x-intercept and y-intercept) so you can plot them on the graph.

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1. y = ½x + 1

- When x = 0 → y = ½(0) + 1 = 1 → Point: (0, 1)
- When y = 0 → 0 = ½x + 1 → ½x = -1 → x = -2 → Point: (-2, 0)

Plot (0,1) and (-2,0), then draw a straight line through them.

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2. y = 3x – 2

- When x = 0 → y = 3(0) – 2 = -2 → Point: (0, -2)
- When y = 0 → 0 = 3x – 2 → 3x = 2 → x = 2/3 → Point: (2/3, 0)

Plot (0,-2) and (2/3, 0). Since 2/3 is about 0.67, go right a little less than 1 unit from origin.

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3. y = ⅔x – 4

- When x = 0 → y = ⅔(0) – 4 = -4 → Point: (0, -4)
- When y = 0 → 0 = ⅔x – 4 → ⅔x = 4 → x = 4 × 3/2 = 6 → Point: (6, 0)

Plot (0,-4) and (6,0).

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4. y = 5x – 4

- When x = 0 → y = 5(0) – 4 = -4 → Point: (0, -4)
- When y = 0 → 0 = 5x – 4 → 5x = 4 → x = 4/5 = 0.8 → Point: (0.8, 0)

Plot (0,-4) and (0.8, 0).

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5. y = -2x – 3

- When x = 0 → y = -2(0) – 3 = -3 → Point: (0, -3)
- When y = 0 → 0 = -2x – 3 → -2x = 3 → x = -3/2 = -1.5 → Point: (-1.5, 0)

Plot (0,-3) and (-1.5, 0).

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6. y = -2

This is a horizontal line! No matter what x is, y is always -2.

→ Draw a flat line across at y = -2.

Points: (0, -2), (1, -2), (-1, -2), etc.

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8. 5x + y = 0

Solve for y: y = -5x

- When x = 0 → y = 0 → Point: (0, 0)
- When x = 1 → y = -5 → Point: (1, -5)

Plot (0,0) and (1,-5).

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10. 3x + 4y = 12

Find intercepts:

- x = 0 → 4y = 12 → y = 3 → Point: (0, 3)
- y = 0 → 3x = 12 → x = 4 → Point: (4, 0)

Plot (0,3) and (4,0).

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12. 4x – 12y = 24

Simplify first? Divide all terms by 4:
→ x – 3y = 6

Now find intercepts:

- x = 0 → -3y = 6 → y = -2 → Point: (0, -2)
- y = 0 → x = 6 → Point: (6, 0)

Plot (0,-2) and (6,0).

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14. y = -⅓x + 1

- When x = 0 → y = 1 → Point: (0, 1)
- When y = 0 → 0 = -⅓x + 1 → ⅓x = 1 → x = 3 → Point: (3, 0)

Plot (0,1) and (3,0).

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16. y = 3x – 1

- When x = 0 → y = -1 → Point: (0, -1)
- When y = 0 → 0 = 3x – 1 → 3x = 1 → x = 1/3 ≈ 0.33 → Point: (0.33, 0)

Plot (0,-1) and (0.33, 0).

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18. -2x + 8y = 16

Solve for y or find intercepts:

- x = 0 → 8y = 16 → y = 2 → Point: (0, 2)
- y = 0 → -2x = 16 → x = -8 → Point: (-8, 0)

Plot (0,2) and (-8,0).

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20. x + y = -2

Find intercepts:

- x = 0 → y = -2 → Point: (0, -2)
- y = 0 → x = -2 → Point: (-2, 0)

Plot (0,-2) and (-2,0).

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Final Answer:
For each equation, plot the two points calculated above and draw a straight line through them. The lines are:

1. Through (0,1) and (-2,0)
2. Through (0,-2) and (2/3,0)
3. Through (0,-4) and (6,0)
4. Through (0,-4) and (0.8,0)
5. Through (0,-3) and (-1.5,0)
6. Horizontal line at y = -2
8. Through (0,0) and (1,-5)
10. Through (0,3) and (4,0)
12. Through (0,-2) and (6,0)
14. Through (0,1) and (3,0)
16. Through (0,-1) and (0.33,0)
18. Through (0,2) and (-8,0)
20. Through (0,-2) and (-2,0)