# How do you find the slope that is perpendicular to the line x-3y=9?

Mar 15, 2017

Any line perpendicular to $x - 3 y = 9$ has a slope of $- 3$

#### Explanation:

A line in the form $A x + B y = C$ has a slope of $m = - \frac{A}{B}$

If a line has a slope of $m$ then every line perpendicular to it has a slope of $- \frac{1}{m}$

For the given example $1 x - 3 y = 9$ has a slope of $- \left(\frac{1}{- 3}\right) = \frac{1}{3}$
and
any line perpendicular to it has a slope of
$\textcolor{w h i t e}{\text{XXX}} - \frac{1}{\left(\frac{1}{3}\right)} = - 3$