Writing Equations From a Table Worksheet - Practice converting tables of values into linear equations in slope-intercept form.

Absolutely! Let’s solve each problem step by step. We are to write the equation in slope-intercept form:
> y = mx + b
where:
- m = slope (rate of change) = (change in y) / (change in x)
- b = y-intercept (value of y when x = 0)

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✔ Problem 1:

| x | y |
|---|---|
| 0 | 6 |
| 1 | 7 |
| 2 | 8 |
| 3 | 9 |
| 4 |10 |

- When x = 0, y = 6 → so b = 6
- Slope m = (7 - 6)/(1 - 0) = 1/1 = 1

✔ Equation: y = 1x + 6 → y = x + 6

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✔ Problem 2:

| x | y |
|---|---|
| 1 | 1 |
| 2 | 5 |
| 3 | 9 |
| 4 |13 |
| 5 |17 |

- Pick two points: (1,1) and (2,5)
→ m = (5 - 1)/(2 - 1) = 4/1 = 4

Now plug into y = mx + b using point (1,1):
1 = 4(1) + b → 1 = 4 + b → b = -3

✔ Equation: y = 4x - 3

*(Check with another point: x=3 → y=4*3 -3 = 12-3=9 ✓)*

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✔ Problem 3:

| x | y |
|---|---|
| 2 |12 |
| 4 |16 |
| 8 |24 |
|10 |28 |

- Use (2,12) and (4,16):
m = (16 - 12)/(4 - 2) = 4/2 = 2

Plug into y = mx + b using (2,12):
12 = 2(2) + b → 12 = 4 + b → b = 8

✔ Equation: y = 2x + 8

*(Check: x=8 → y=2*8+8=24 ✓)*

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✔ Problem 4:

| x | y |
|---|---|
| 0 | 0 |
| 1 | 6 |
| 2 |12 |
| 3 |18 |

- When x=0, y=0 → b = 0
- m = (6 - 0)/(1 - 0) = 6 → m = 6

✔ Equation: y = 6x

*(Check: x=2 → y=12 ✓)*

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✔ Problem 5:

| x | y |
|---|---|
| 5 | 4 |
|20 |10 |
|30 |14 |
|35 |16 |

Use (5,4) and (20,10):
m = (10 - 4)/(20 - 5) = 6/15 = 2/5

Now plug into y = mx + b using (5,4):
4 = (2/5)(5) + b → 4 = 2 + b → b = 2

✔ Equation: y = (2/5)x + 2

*(Check: x=30 → y=(2/5)*30 + 2 = 12 + 2 = 14 ✓)*

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✔ Problem 6:

| x | y |
|---|---|
| 0 | 3 |
| 1 | 7 |
| 2 |11 |
| 3 |15 |

- When x=0, y=3 → b = 3
- m = (7 - 3)/(1 - 0) = 4 → m = 4

✔ Equation: y = 4x + 3

*(Check: x=2 → y=8+3=11 ✓)*

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## 📝 Final Answers:

1. y = x + 6
2. y = 4x - 3
3. y = 2x + 8
4. y = 6x
5. y = (2/5)x + 2
6. y = 4x + 3

Let me know if you’d like a graph or further explanation for any!