# What is the slope of the line perpendicular to 8x - 3y = -5?

Apr 7, 2018

$m ' = - \frac{1}{4}$

#### Explanation:

To find the slope of the line perpendicular to any line $l$, you must first find the slope of $l$.

To find the slope of $8 x - 3 y = - 5$, we manipulate it into slope-intercept form, $y = m x + b$.

$8 x - 2 y = - 5$,
$- 2 y = - 5 - 8 x$,
$2 y = 5 + 8 x$
$y = \frac{5}{2} + 4 x$,
$y = 4 x + \frac{5}{2}$.

We see that the slope of our given line, then, is $m = 4$. The slope of the line perpendicular to a line with slope $m$ is given by $m ' = - \frac{1}{m}$. So the slope we are looking for is $m ' = - \frac{1}{m} = - \frac{1}{4}$.