Graphing Linear Equations Worksheets with Answer Key - Free Printable

Let’s go through each problem one by one. For each, we’ll:

1. Use the given equation to fill in the missing y-values for each x-value (or vice versa).
2. Then plot those points on the graph and draw the line.

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Problem ①: x + 12 = 6y

We need to solve for y in terms of x:
→ y = (x + 12) / 6

Now plug in each x:

- x = -12 → y = (-12 + 12)/6 = 0/6 = 0
- x = -6 → y = (-6 + 12)/6 = 6/6 = 1
- x = 0 → y = (0 + 12)/6 = 12/6 = 2
- x = 6 → y = (6 + 12)/6 = 18/6 = 3
- x = 12 → y = (12 + 12)/6 = 24/6 = 4

Table filled:
| x | y |
|----|---|
| -12| 0 |
| -6 | 1 |
| 0 | 2 |
| 6 | 3 |
| 12 | 4 |

Plot these points: (-12,0), (-6,1), (0,2), (6,3), (12,4) — they should form a straight line.

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Problem ②: y = 3x + 1

Plug in each x:

- x = 1 → y = 3(1) + 1 = 4
- x = 0 → y = 3(0) + 1 = 1
- x = -1 → y = 3(-1) + 1 = -3 + 1 = -2
- x = -2 → y = 3(-2) + 1 = -6 + 1 = -5

Table filled:
| x | y |
|----|---|
| 1 | 4 |
| 0 | 1 |
| -1 | -2|
| -2 | -5|

Plot: (1,4), (0,1), (-1,-2), (-2,-5)

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Problem ③: y = (3/4)x

Multiply each x by 3/4:

- x = -4 → y = (3/4)(-4) = -3
- x = 0 → y = (3/4)(0) = 0
- x = 2 → y = (3/4)(2) = 6/4 = 1.5
- x = 4 → y = (3/4)(4) = 3

Table filled:
| x | y |
|----|-----|
| -4 | -3 |
| 0 | 0 |
| 2 | 1.5 |
| 4 | 3 |

Plot: (-4,-3), (0,0), (2,1.5), (4,3)

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Problem ④: y = -2x + 2

Plug in each x:

- x = -2 → y = -2(-2) + 2 = 4 + 2 = 6
- x = 1 → y = -2(1) + 2 = -2 + 2 = 0
- x = 3 → y = -2(3) + 2 = -6 + 2 = -4
- x = 0 → y = -2(0) + 2 = 2

Table filled:
| x | y |
|----|---|
| -2 | 6 |
| 1 | 0 |
| 3 | -4|
| 0 | 2 |

Plot: (-2,6), (1,0), (3,-4), (0,2)

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Problem ⑤: y = -x

Just flip the sign of x:

- x = 5 → y = -5
- x = 0 → y = 0
- x = -1 → y = 1
- x = -3 → y = 3

Table filled:
| x | y |
|----|---|
| 5 | -5|
| 0 | 0 |
| -1 | 1 |
| -3 | 3 |

Plot: (5,-5), (0,0), (-1,1), (-3,3)

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Problem ⑥: y = 3x

Multiply x by 3:

- x = -1 → y = 3(-1) = -3
- x = 1 → y = 3(1) = 3
- x = 0 → y = 3(0) = 0
- x = 1.5 → y = 3(1.5) = 4.5

Table filled:
| x | y |
|-----|-----|
| -1 | -3 |
| 1 | 3 |
| 0 | 0 |
| 1.5 | 4.5 |

Plot: (-1,-3), (1,3), (0,0), (1.5,4.5)

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✔ All tables are now complete with correct y-values calculated from the equations.

Final Answer:
The completed tables are as follows:

① y-values: 0, 1, 2, 3, 4
② y-values: 4, 1, -2, -5
③ y-values: -3, 0, 1.5, 3
④ y-values: 6, 0, -4, 2
⑤ y-values: -5, 0, 1, 3
⑥ y-values: -3, 3, 0, 4.5

Plot each set of points on their respective graphs and draw a straight line through them.