# How do you find the slope that is perpendicular to the line  5x-3y=8?

Apr 7, 2018

$\text{perpendicular slope } = - \frac{3}{5}$

#### Explanation:

$\text{establish the slope of the given line}$

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{rearrange "5x-3y=8" into this form}$

$\Rightarrow 3 y = 5 x - 8 \Rightarrow y = \frac{5}{3} x - \frac{8}{3}$

$\text{with slope m } = \frac{5}{3}$

$\text{Given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{\frac{5}{3}} = - \frac{3}{5}$