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

Jul 18, 2016

Slope of the perpendicular: $\textcolor{g r e e n}{\frac{1}{3}}$

#### Explanation:

The standard general form of a linear equation in slope-intercept form is:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$
with slope $\textcolor{g r e e n}{m}$ and y-intercept $\textcolor{b l u e}{b}$.

The given equation $y = \left(- 3 x\right)$
can be re-written to be in explicit slope-intercept form as:
$\textcolor{w h i t e}{\text{XXX")y=color(green)(} \left(- 3\right)} x + \textcolor{b l u e}{0}$
with slope color(green)(""(-3))

If a line has a slope of color(m)
then all lines perpendicular to it have a slope of color(green)(""(-1/m))

Since $y = - 3 x$ has a slope of $\textcolor{g r e e n}{m = - 3}$
any line perpendicular to it will have a slope of
color(white)("XXX")color(green)((-1/m)=-(1/(-3))=1/3