# How do you write an equation through point (6, -8), perpendicular to y= -6x - 9?

Sep 11, 2017

$x - 6 y = 42$

#### Explanation:

$y = \textcolor{b l u e}{- 6} x - 9$ is an equation in slope-intercept form with a slope of color(blue)(""(-6)).

Any line perpendicular to it must have a slope of $- \frac{1}{\textcolor{b l u e}{- 6}} = \textcolor{m a \ge n t a}{\frac{1}{6}}$

If the required perpendicular line passes through $\left(\textcolor{red}{6} , \textcolor{b r o w n}{- 8}\right)$
then, in slope-point form, its equation can be written as
$y - \left(\textcolor{b r o w n}{-} 8\right) = \textcolor{m a \ge n t a}{\frac{1}{6}} \left(x - \textcolor{red}{6}\right)$

Simplifying
$6 \left(y + 8\right) = x - 6$

$6 y + 48 = x - 6$

$x - 6 y = 42$