Worksheet for graphing linear equations with blank coordinate grids and tables.

Let’s solve each problem step by step. We’re given linear equations in the form y = mx + b, and we need to fill in a table of values (x and y) and then graph the line.

We’ll do this for all 6 problems, one at a time.

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Problem 1: y = -½x + 3

We pick x-values from the table: -4, -2, 0, 2, 4

Plug into equation:

- x = -4 → y = -½(-4) + 3 = 2 + 3 = 5
- x = -2 → y = -½(-2) + 3 = 1 + 3 = 4
- x = 0 → y = -½(0) + 3 = 0 + 3 = 3
- x = 2 → y = -½(2) + 3 = -1 + 3 = 2
- x = 4 → y = -½(4) + 3 = -2 + 3 = 1

Table:
| x | y |
|---|---|
|-4 | 5 |
|-2 | 4 |
| 0 | 3 |
| 2 | 2 |
| 4 | 1 |

Plot these points and draw a straight line through them.

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Problem 2: y = ⅓x - 1

x-values: -6, -3, 0, 3, 6

Calculate:

- x = -6 → y = ⅓(-6) - 1 = -2 - 1 = -3
- x = -3 → y = ⅓(-3) - 1 = -1 - 1 = -2
- x = 0 → y = ⅓(0) - 1 = 0 - 1 = -1
- x = 3 → y = ⅓(3) - 1 = 1 - 1 = 0
- x = 6 → y = ⅓(6) - 1 = 2 - 1 = 1

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

Plot and connect.

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Problem 3: y = -¾x + 2

x-values: -4, -2, 0, 2, 4

Calculate:

- x = -4 → y = -¾(-4) + 2 = 3 + 2 = 5
- x = -2 → y = -¾(-2) + 2 = 1.5 + 2 = 3.5 → or 7/2
- x = 0 → y = -¾(0) + 2 = 0 + 2 = 2
- x = 2 → y = -¾(2) + 2 = -1.5 + 2 = 0.5 → or 1/2
- x = 4 → y = -¾(4) + 2 = -3 + 2 = -1

Table:
| x | y |
|---|-----|
|-4 | 5 |
|-2 | 3.5 |
| 0 | 2 |
| 2 | 0.5 |
| 4 | -1 |

You can write decimals or fractions — both are fine. Plot and connect.

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Problem 4: y = ⅔x - 2

x-values: -6, -3, 0, 3, 6

Calculate:

- x = -6 → y = ⅔(-6) - 2 = -4 - 2 = -6
- x = -3 → y = ⅔(-3) - 2 = -2 - 2 = -4
- x = 0 → y = ⅔(0) - 2 = 0 - 2 = -2
- x = 3 → y = ⅔(3) - 2 = 2 - 2 = 0
- x = 6 → y = ⅔(6) - 2 = 4 - 2 = 2

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

Plot and connect.

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Problem 5: y = -¼x + 1

x-values: -8, -4, 0, 4, 8

Calculate:

- x = -8 → y = -¼(-8) + 1 = 2 + 1 = 3
- x = -4 → y = -¼(-4) + 1 = 1 + 1 = 2
- x = 0 → y = -¼(0) + 1 = 0 + 1 = 1
- x = 4 → y = -¼(4) + 1 = -1 + 1 = 0
- x = 8 → y = -¼(8) + 1 = -2 + 1 = -1

Table:
| x | y |
|---|---|
|-8 | 3 |
|-4 | 2 |
| 0 | 1 |
| 4 | 0 |
| 8 | -1 |

Plot and connect.

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Problem 6: y = ½x - 3

x-values: -4, -2, 0, 2, 4

Calculate:

- x = -4 → y = ½(-4) - 3 = -2 - 3 = -5
- x = -2 → y = ½(-2) - 3 = -1 - 3 = -4
- x = 0 → y = ½(0) - 3 = 0 - 3 = -3
- x = 2 → y = ½(2) - 3 = 1 - 3 = -2
- x = 4 → y = ½(4) - 3 = 2 - 3 = -1

Table:
| x | y |
|---|---|
|-4 |-5 |
|-2 |-4 |
| 0 |-3 |
| 2 |-2 |
| 4 |-1 |

Plot and connect.

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Final Answer:
All tables filled correctly as shown above. Graph each set of points on its coordinate plane and draw a straight line through them. Each line represents the given linear equation.