# How do you find the slope that is perpendicular to the line y=1/3x+6?

Jun 29, 2016

Slope: $\textcolor{red}{- 3}$

#### Explanation:

If a line has a slope of $\textcolor{g r e e n}{m}$
then any line perpendicular to it has a slope of $\textcolor{red}{- \frac{1}{m}}$

Equations in the form:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$
are in "slope-intercept form" with a slope of $\textcolor{g r e e n}{m}$

The given equation:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{\frac{1}{3}} x + \textcolor{b l u e}{6}$
is in this "slope-intercept form" with a slope of $\textcolor{g r e e n}{\frac{1}{3}}$

Any line perpendicular to it has a slope of
$\textcolor{w h i t e}{\text{XXX")color(red)(-1/(} \left(\frac{1}{3}\right)} = - 3$