Question

What is the equation of a line perpendicular to

Answer 1

Since the given line

$y = \frac{ 1}{4} x - 3$

has slope
$= \frac{1}{4}$


The equation of the line perpendicular to it must have a slope which is the negative reciprocal of ,
$\frac{1}{4}$
The slope of the perpendicular line
$= \frac{ - 1}{ \frac{1}{4} } = - 4$
Using the slope intercept form,

$y = mx + c$
We substitute
$- 4$
This implies that,
$y = - 4x + c$
Since

$(-2,4)$
lies on this line , it must satisfy its equation.

That is

$4 = - 4( - 2) + c$


This implies that

$4 = 8 + c$
$4 - 8 = c$
$c = - 4$

The line therefore has equation,

$y = - 4x - 4$