Worksheet Works Graphing Linear Equations 1 | Download Free PDF ... - Free Printable

Let’s solve each problem step by step. For each equation, we’ll plug in the given x-values to find y, then you can graph the points on the coordinate plane.

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Problem (1): y = 4x

Given x values: -1½, ½, 0, 1

- When x = -1½ → y = 4 × (-1.5) = -6
- When x = ½ → y = 4 × 0.5 = 2
- When x = 0 → y = 4 × 0 = 0
- When x = 1 → y = 4 × 1 = 4

Table for (1):
| x | y |
|-------|-----|
| -1½ | -6 |
| ½ | 2 |
| 0 | 0 |
| 1 | 4 |

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Problem (2): y = x + 6

Given x values: -4, -3, -2, 1

- x = -4 → y = -4 + 6 = 2
- x = -3 → y = -3 + 6 = 3
- x = -2 → y = -2 + 6 = 4
- x = 1 → y = 1 + 6 = 7

Table for (2):
| x | y |
|----|----|
| -4 | 2 |
| -3 | 3 |
| -2 | 4 |
| 1 | 7 |

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Problem (3): y = (1/3)x - 4

Given x values: -7, -5, -1, 1

We’ll calculate carefully:

- x = -7 → y = (1/3)(-7) - 4 = -7/3 - 4 = -7/3 - 12/3 = -19/3 ≈ -6.33
But since this is a worksheet, maybe they expect fractions? Let’s keep as fraction: -19/3

Wait — let me double-check if these x-values are chosen to give nice answers. Maybe I made a mistake?

Actually, let’s recalculate with decimals or see if it simplifies:

(1/3)(-7) = -2.333..., minus 4 = -6.333... → yes, -19/3

But perhaps the worksheet expects exact fractions. We’ll write them as fractions.

- x = -7 → y = (1/3)(-7) - 4 = -7/3 - 12/3 = -19/3
- x = -5 → y = (1/3)(-5) - 4 = -5/3 - 12/3 = -17/3
- x = -1 → y = (1/3)(-1) - 4 = -1/3 - 12/3 = -13/3
- x = 1 → y = (1/3)(1) - 4 = 1/3 - 12/3 = -11/3

Hmm, those are messy. But mathematically correct. Maybe the worksheet intends for students to use decimal approximations? Or perhaps I misread the equation?

Looking back: “y = ⅓x – 4” — yes.

Alternatively, maybe the x-values were meant to be multiples of 3? But they’re not. So we proceed.

Table for (3):
| x | y |
|----|---------|
| -7 | -19/3 |
| -5 | -17/3 |
| -1 | -13/3 |
| 1 | -11/3 |

Or as mixed numbers:
- -19/3 = -6⅓
- -17/3 = -5⅔
- -13/3 = -4⅓
- -11/3 = -3⅔

But unless specified, improper fractions are fine.

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Problem (4): y = (1/4)x + 1

Given x values: -6, -4, 0, 5

Calculate:

- x = -6 → y = (1/4)(-6) + 1 = -6/4 + 1 = -3/2 + 1 = -1.5 + 1 = -0.5 or -1/2
- x = -4 → y = (1/4)(-4) + 1 = -1 + 1 = 0
- x = 0 → y = 0 + 1 = 1
- x = 5 → y = (1/4)(5) + 1 = 5/4 + 1 = 1.25 + 1 = 2.25 or 9/4

Table for (4):
| x | y |
|----|------|
| -6 | -1/2 |
| -4 | 0 |
| 0 | 1 |
| 5 | 9/4 |

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Problem (5): y = (1/2)x - 6

Given x values: 1, 2, 3, 6

- x = 1 → y = 0.5 - 6 = -5.5 or -11/2
- x = 2 → y = 1 - 6 = -5
- x = 3 → y = 1.5 - 6 = -4.5 or -9/2
- x = 6 → y = 3 - 6 = -3

Table for (5):
| x | y |
|---|-------|
| 1 | -11/2 |
| 2 | -5 |
| 3 | -9/2 |
| 6 | -3 |

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Problem (6): y = (1/3)x - 6

Given x values: -3, 1, 2, 7

- x = -3 → y = (1/3)(-3) - 6 = -1 - 6 = -7
- x = 1 → y = (1/3)(1) - 6 = 1/3 - 6 = 1/3 - 18/3 = -17/3
- x = 2 → y = (1/3)(2) - 6 = 2/3 - 18/3 = -16/3
- x = 7 → y = (1/3)(7) - 6 = 7/3 - 18/3 = -11/3

Table for (6):
| x | y |
|----|---------|
| -3 | -7 |
| 1 | -17/3 |
| 2 | -16/3 |
| 7 | -11/3 |

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Now, after checking all calculations again for accuracy:

✔ Problem (1): All correct
✔ Problem (2): All correct
✔ Problem (3): Fractions are correct even if messy
✔ Problem (4): Correct
✔ Problem (5): Correct
✔ Problem (6): Correct

You can now plot each (x, y) pair on the graph provided next to each table. Connect the points with a straight line for each equation.

Final Answer:

Completed tables:

(1)
| x | y |
|-------|-----|
| -1½ | -6 |
| ½ | 2 |
| 0 | 0 |
| 1 | 4 |

(2)
| x | y |
|----|----|
| -4 | 2 |
| -3 | 3 |
| -2 | 4 |
| 1 | 7 |

(3)
| x | y |
|----|---------|
| -7 | -19/3 |
| -5 | -17/3 |
| -1 | -13/3 |
| 1 | -11/3 |

(4)
| x | y |
|----|------|
| -6 | -1/2 |
| -4 | 0 |
| 0 | 1 |
| 5 | 9/4 |

(5)
| x | y |
|---|-------|
| 1 | -11/2 |
| 2 | -5 |
| 3 | -9/2 |
| 6 | -3 |

(6)
| x | y |
|----|---------|
| -3 | -7 |
| 1 | -17/3 |
| 2 | -16/3 |
| 7 | -11/3 |