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 and draw the line.

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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 compute carefully:

- x = -7 → y = (1/3)(-7) – 4 = -7/3 – 4 = -7/3 – 12/3 = -19/3 ≈ -6.333...
But since this is a worksheet, maybe they want fractions? Let’s keep as fraction: -19/3

Wait — let me 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.

Alternatively, perhaps the problem expects exact fractions.

But looking at other problems, maybe we should just calculate exactly.

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 that’s what the math gives us.

Alternatively, maybe the problem has a typo? Or perhaps we’re supposed to leave as fractions.

I think we have to go with the math.

So table for (3):

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

But wait — let me double-check problem (3). The equation is y = (1/3)x – 4. Yes.

Maybe the x-values are meant to be multiples of 3? But they’re not. So we proceed.

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

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

- 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: 1, 2, 3, 6

- x = 1 → y = 0.5(1) – 6 = 0.5 – 6 = -5.5 or -11/2
- x = 2 → y = 0.5(2) – 6 = 1 – 6 = -5
- x = 3 → y = 0.5(3) – 6 = 1.5 – 6 = -4.5 or -9/2
- x = 6 → y = 0.5(6) – 6 = 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: -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, let’s verify all calculations one more time to avoid mistakes.

✔ Problem (1): y=4x → correct.

✔ Problem (2): y=x+6 → correct.

✔ Problem (3): y=(1/3)x–4 → all fractions correct.

✔ Problem (4): y=(1/4)x+1 →
- x=-6: -6/4 = -3/2; -3/2 + 1 = -1/2 ✔️
- x=-4: -1 +1 =0 ✔️
- x=0: 1 ✔️
- x=5: 5/4 + 4/4 = 9/4 ✔️

✔ Problem (5): y=(1/2)x–6 →
- x=1: 0.5–6=-5.5 ✔️
- x=2: 1–6=-5 ✔️
- x=3: 1.5–6=-4.5 ✔️
- x=6: 3–6=-3 ✔️

✔ Problem (6): y=(1/3)x–6 →
- x=-3: -1–6=-7 ✔️
- x=1: 1/3–6= -17/3 ✔️
- x=2: 2/3–6= -16/3 ✔️
- x=7: 7/3–6= -11/3 ✔️

All correct.

Final Answer:

Here are the completed tables for each problem:

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

(2) y = x + 6
| x | y |
|----|----|
| -4 | 2 |
| -3 | 3 |
| -2 | 4 |
| 1 | 7 |

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

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

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

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

You can now plot these points on the graphs and draw straight lines through them. Remember: linear equations always make straight lines!