# How do you write an equation of a line passing through (0, -5), perpendicular to 4x+y=0 ?

Jul 27, 2016

$x - 4 y = 20$

#### Explanation:

For the general case:
$\textcolor{w h i t e}{\text{XXX}} A x + B y = C$ has a slope of $m = - \frac{A}{B}$

So $4 x + 1 = 0$ has a slope of $m = - 4$

In general if a line has a slope of $m$ all lines perpendicular to it will have a slope of $- \frac{1}{m}$

There any line perpendicular to $4 x + y = 0$ will have a slope of $\frac{1}{4}$.

If such a perpendicular line passes through $\left(0 , - 5\right)$
then using the slope-point form:
$\textcolor{w h i t e}{\text{XXX}} y - \left(- 5\right) = \frac{1}{4} \left(x - 0\right)$
or
$\textcolor{w h i t e}{\text{XXX}} x - 4 y = 20$