Find the Slope of a Perpendicular Line 5x-y=9

$5 x - y = 9$

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 $5 x$ from both sides of the equation.

$- y = 9 - 5 x$

Divide each term in $- y = 9 - 5 x$ by $- 1$ and simplify.

Divide each term in $- y = 9 - 5 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{9}{- 1} + \frac{- 5 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{9}{- 1} + \frac{- 5 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{9}{- 1} + \frac{- 5 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $9$ by $- 1$ .

$y = - 9 + \frac{- 5 x}{- 1}$

Move the negative one from the denominator of $\frac{- 5 x}{- 1}$ .

$y = - 9 - 1 \cdot (- 5 x)$

Rewrite $- 1 \cdot (- 5 x)$ as $- (- 5 x)$ .

$y = - 9 - (- 5 x)$

Multiply $- 5$ by $- 1$ .

$y = - 9 + 5 x$

Reorder $- 9$ and $5 x$ .

$y = 5 x - 9$

Step 2

Using the slope-intercept form, the slope is $5$ .

$m = 5$

Step 3

The equation of a perpendicular line to $y = 5 x - 9$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{5}$

Step 4