Write Linear Equations From Tables worksheet with six practice problems involving x and y values.

Let's solve each table step by step to find the linear equation in the form:

$$
y = mx + b
$$

Where:
- $ m $ is the slope
- $ b $ is the y-intercept

We'll use the given $ x $ and $ y $ values to find the pattern.

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Table 1

| x | y |
|---|---|
| 3 | 18 |
| 4 | 24 |
| 5 | 30 |

Step 1: Find the slope (m)
Use two points: (3, 18) and (4, 24)

$$
m = \frac{24 - 18}{4 - 3} = \frac{6}{1} = 6
$$

Step 2: Use point-slope form or plug into $ y = mx + b $
Use (3, 18):

$$
18 = 6(3) + b \Rightarrow 18 = 18 + b \Rightarrow b = 0
$$

✔ Equation: $ y = 6x $

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Table 2

| x | y |
|---|---|
| 7 | 11 |
| 8 | 12 |
| 9 | 13 |

Slope:

$$
m = \frac{12 - 11}{8 - 7} = \frac{1}{1} = 1
$$

Use (7, 11):

$$
11 = 1(7) + b \Rightarrow 11 = 7 + b \Rightarrow b = 4
$$

✔ Equation: $ y = x + 4 $

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Table 3

| x | y |
|---|---|
| 5 | 12 |
| 6 | 15 |
| 7 | 18 |
| 11 | 30 |

Slope:

$$
m = \frac{15 - 12}{6 - 5} = \frac{3}{1} = 3
$$

Use (5, 12):

$$
12 = 3(5) + b \Rightarrow 12 = 15 + b \Rightarrow b = -3
$$

✔ Equation: $ y = 3x - 3 $

Check with (11, 30):
$ y = 3(11) - 3 = 33 - 3 = 30 $ ✔

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Table 4

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

Slope:

$$
m = \frac{9 - 5}{2 - 1} = \frac{4}{1} = 4
$$

Use (1, 5):

$$
5 = 4(1) + b \Rightarrow 5 = 4 + b \Rightarrow b = 1
$$

✔ Equation: $ y = 4x + 1 $

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Table 5

| x | y |
|---|---|
| 4 | 16 |
| 5 | 20 |
| 7 | ? |

Slope:

$$
m = \frac{20 - 16}{5 - 4} = \frac{4}{1} = 4
$$

Use (4, 16):

$$
16 = 4(4) + b \Rightarrow 16 = 16 + b \Rightarrow b = 0
$$

✔ Equation: $ y = 4x $

Now fill in missing value for $ x = 7 $:

$$
y = 4(7) = 28
$$

✔ Missing value: 28

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Table 6

| x | y |
|---|---|
| 2 | 11 |
| 4 | 13 |
| 6 | ? |
| 7 | 17 |

Slope:

$$
m = \frac{13 - 11}{4 - 2} = \frac{2}{2} = 1
$$

Use (2, 11):

$$
11 = 1(2) + b \Rightarrow 11 = 2 + b \Rightarrow b = 9
$$

✔ Equation: $ y = x + 9 $

Now find missing value at $ x = 6 $:

$$
y = 6 + 9 = 15
$$

✔ Missing value: 15

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Table 7

| x | y |
|---|---|
| 5 | 45 |
| 6 | ? |
| 7 | 63 |
| 73 | ? |

Slope:

Use (5, 45) and (7, 63):

$$
m = \frac{63 - 45}{7 - 5} = \frac{18}{2} = 9
$$

Use (5, 45):

$$
45 = 9(5) + b \Rightarrow 45 = 45 + b \Rightarrow b = 0
$$

✔ Equation: $ y = 9x $

Now fill in missing values:

- $ x = 6 $: $ y = 9(6) = 54 $
- $ x = 73 $: $ y = 9(73) = 657 $

✔ Missing values: 54 and 657

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Table 8

| x | y |
|---|---|
| 3 | 18 |
| 5 | 20 |
| 7 | ? |
| 24 | ? |

Slope:

Use (3, 18) and (5, 20):

$$
m = \frac{20 - 18}{5 - 3} = \frac{2}{2} = 1
$$

Use (3, 18):

$$
18 = 1(3) + b \Rightarrow 18 = 3 + b \Rightarrow b = 15
$$

✔ Equation: $ y = x + 15 $

Now find missing values:

- $ x = 7 $: $ y = 7 + 15 = 22 $
- $ x = 24 $: $ y = 24 + 15 = 39 $

✔ Missing values: 22 and 39

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✔ Final Answers:

#### Equations:
1. $ y = 6x $
2. $ y = x + 4 $
3. $ y = 3x - 3 $
4. $ y = 4x + 1 $
5. $ y = 4x $
6. $ y = x + 9 $
7. $ y = 9x $
8. $ y = x + 15 $

#### Missing Values:
- Table 5: $ x = 7 $ → $ y = 28 $
- Table 6: $ x = 6 $ → $ y = 15 $
- Table 7: $ x = 6 $ → $ y = 54 $, $ x = 73 $ → $ y = 657 $
- Table 8: $ x = 7 $ → $ y = 22 $, $ x = 24 $ → $ y = 39 $

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