Pre-Algebra Examples

$y - 5 = \frac{1}{8} x - \frac{1}{2}$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the right side.

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Step 1.2.1

Combine $\frac{1}{8}$ and $x$ .

$y - 5 = \frac{x}{8} - \frac{1}{2}$

Step 1.3

Move all terms not containing $y$ to the right side of the equation.

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Step 1.3.1

Add $5$ to both sides of the equation.

$y = \frac{x}{8} - \frac{1}{2} + 5$

Step 1.3.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{x}{8} - \frac{1}{2} + 5 \cdot \frac{2}{2}$

Step 1.3.3

Combine $5$ and $\frac{2}{2}$ .

$y = \frac{x}{8} - \frac{1}{2} + \frac{5 \cdot 2}{2}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = \frac{x}{8} + \frac{- 1 + 5 \cdot 2}{2}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $5$ by $2$ .

$y = \frac{x}{8} + \frac{- 1 + 10}{2}$

Step 1.3.5.2

Add $- 1$ and $10$ .

$y = \frac{x}{8} + \frac{9}{2}$

Step 1.4

Reorder terms.

$y = \frac{1}{8} x + \frac{9}{2}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{8}$ .

$m = \frac{1}{8}$

Step 3