Find the Slope of a Parallel Line x-3y=24

$x - 3 y = 24$

Step 1

Rewrite in slope-intercept form.

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

$y = m x + b$

Subtract $x$ from both sides of the equation.

$- 3 y = 24 - x$

Divide each term in $- 3 y = 24 - x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 24 - x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{24}{- 3} + \frac{- x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{24}{- 3} + \frac{- x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{24}{- 3} + \frac{- x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $24$ by $- 3$ .

$y = - 8 + \frac{- x}{- 3}$

Dividing two negative values results in a positive value.

$y = - 8 + \frac{x}{3}$

Write in $y = m x + b$ form.

Reorder $- 8$ and $\frac{x}{3}$ .

$y = \frac{x}{3} - 8$

Reorder terms.

$y = \frac{1}{3} x - 8$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{3}$ .

$m = \frac{1}{3}$

Step 3

All lines that are parallel to $y = \frac{1}{3} x - 8$ have the same slope of $\frac{1}{3}$ .

$m_{parallel} = \frac{1}{3}$

Step 4