Write An Equation From A Table Worksheets [PDF] (8.F.A.3): 8th ... - Free Printable

Let's solve each problem step by step.

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Problem 1

We are given a table of values:

| $ x $ | $ y $ |
|--------|-------------|
| -15 | $-\frac{13}{2}$ |
| -12 | -4 |
| -9 | $-\frac{3}{2}$ |
| -6 | 1 |

We need to find the equation of the line in slope-intercept form:
$$
y = mx + b
$$
where $ m $ is the slope and $ b $ is the y-intercept.

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#### Step 1: Find the slope $ m $

Use two points from the table. Let's pick $(-15, -\frac{13}{2})$ and $(-12, -4)$.

$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-\frac{13}{2})}{-12 - (-15)} = \frac{-4 + \frac{13}{2}}{3}
$$

Convert $-4$ to fraction: $-\frac{8}{2}$

$$
= \frac{-\frac{8}{2} + \frac{13}{2}}{3} = \frac{\frac{5}{2}}{3} = \frac{5}{2} \cdot \frac{1}{3} = \frac{5}{6}
$$

So, slope $ m = \frac{5}{6} $

Let’s verify with another pair to confirm consistency.

Use $(-9, -\frac{3}{2})$ and $(-6, 1)$:

$$
m = \frac{1 - (-\frac{3}{2})}{-6 - (-9)} = \frac{1 + \frac{3}{2}}{3} = \frac{\frac{5}{2}}{3} = \frac{5}{6}
$$

Same slope — good!

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#### Step 2: Use point-slope form to find $ b $

Use the point $(-6, 1)$ and $ m = \frac{5}{6} $:

$$
y = mx + b \Rightarrow 1 = \frac{5}{6}(-6) + b
$$

$$
1 = -5 + b \Rightarrow b = 6
$$

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#### ✔ Final Equation for Problem 1:
$$
\boxed{y = \frac{5}{6}x + 6}
$$

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Problem 2

Given table:

| $ x $ | $ y $ |
|--------|--------------|
| 25 | $-\frac{31}{3}$ |
| 21 | -13 |
| 20 | $-\frac{41}{3}$ |
| 15 | -17 |

Again, find $ y = mx + b $

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#### Step 1: Find the slope $ m $

Use points $ (25, -\frac{31}{3}) $ and $ (21, -13) $

First, write $-13$ as $-\frac{39}{3}$ to have common denominator.

$$
m = \frac{-13 - (-\frac{31}{3})}{21 - 25} = \frac{-13 + \frac{31}{3}}{-4}
$$

Convert $-13$ to $-\frac{39}{3}$:

$$
= \frac{-\frac{39}{3} + \frac{31}{3}}{-4} = \frac{-\frac{8}{3}}{-4} = \frac{-8}{3} \cdot \frac{1}{-4} = \frac{8}{12} = \frac{2}{3}
$$

So, $ m = \frac{2}{3} $

Check with another pair: $ (20, -\frac{41}{3}) $ and $ (15, -17) $

Convert $-17$ to $-\frac{51}{3}$

$$
m = \frac{-17 - (-\frac{41}{3})}{15 - 20} = \frac{-17 + \frac{41}{3}}{-5}
= \frac{-\frac{51}{3} + \frac{41}{3}}{-5} = \frac{-\frac{10}{3}}{-5} = \frac{-10}{3} \cdot \frac{1}{-5} = \frac{10}{15} = \frac{2}{3}
$$

Confirmed! Slope $ m = \frac{2}{3} $

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#### Step 2: Find $ b $ using a point

Use $ (15, -17) $:

$$
y = mx + b \Rightarrow -17 = \frac{2}{3}(15) + b
$$

$$
-17 = 10 + b \Rightarrow b = -27
$$

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#### ✔ Final Equation for Problem 2:
$$
\boxed{y = \frac{2}{3}x - 27}
$$

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✔ Final Answers:

1. $ \boxed{y = \frac{5}{6}x + 6} $

2. $ \boxed{y = \frac{2}{3}x - 27} $