Find the Slope of a Perpendicular Line y=-2/5x+8

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

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.

$y = m x + b$

Simplify the right side.

Simplify each term.

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

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

Move $2$ to the left of $x$ .

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{2}{5}$ .

$m = - \frac{2}{5}$

Step 3

The equation of a perpendicular line to $y = - \frac{2}{5} x + 8$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{2}{5}}$

Step 4

Simplify the result.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{2}{5}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{2}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{5}{2})$

Multiply $\frac{5}{2}$ by $1$ .

$m_{perpendicular} = \frac{5}{2}$

Multiply $- - \frac{5}{2}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{5}{2})$

Multiply $\frac{5}{2}$ by $1$ .

$m_{perpendicular} = \frac{5}{2}$

Step 5