# How do you find a standard form equation for the line with (-2, 2); perpendicular to y = 4?

Jun 13, 2017

When given a line of the form, $a x + b y = c$, you can make a perpendicular line by:

Swap "a" and "b": $b x + a y = c$

Make "a" negative: $b x - a y = c$

Set it equal to an unknown constant: $b x - a y = k$

#### Explanation:

Given: $y = 4 \text{ [1]}$

Standard form for equation [1] is:

$0 x + y = 4$

To make a perpendicular line:

Swap "a" and "b":

$x + 0 y = 4$

Make "a" negative:

$x - 0 y = 4$

Set it equal to and unknown constant:

$x - 0 y = k$

Use the point $\left(- 2 , 2\right)$ to find the value of k:

$- 2 - 0 \left(2\right) = k$

$k = - 2$

The standard form is:

$x - 0 y = - 2$