# How do you write an equation of a line perpendicular to y=1/4x+2 and passes through (0,0)?

Nov 11, 2016

$\textcolor{g r e e n}{y = - 4 x}$

#### Explanation:

The given equation : $y = \textcolor{red}{\frac{1}{4}} x + \textcolor{b l u e}{2}$
is in slope-intercept form with slope $\textcolor{red}{\frac{1}{4}}$

If a line has slope $\textcolor{red}{m}$ then all lines perpendicular to it have slopes of $\textcolor{m a \ge n t a}{- \frac{1}{m}}$

Therefore any line perpendicular to the given line must have a slope of $\textcolor{m a \ge n t a}{- 4}$
and since the requested line is to pass through $\left(0 , 0\right)$ (which implies a y-intercept of $\textcolor{b l u e}{0}$
in slope-intercept form this line must have an equation:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{m a \ge n t a}{- 4} x + \textcolor{b l u e}{0}$
or just
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{m a \ge n t a}{- 4} x$