# What are the equations of 2 lines that are perpendicular to the line: 4x+y-2 = 0?

Nov 15, 2015

$y = \frac{1}{4} x + b$

($b$ can be any number)

#### Explanation:

Lets rewrite the equation $4 x + y - 2 = 0$ to solve for y.

$4 x + y - 2 = 0$
$4 x + y = 2$
$y = - 4 x + 2$

This new equation now fits into the helpful format $y = m x + b$

With this formula $b$ is equal to the y intercept and $m$ is equal to the slope.

So if our slope is $- 4$ then to calculate a perpendicular line we flip the number and change the sign. So $- \frac{4}{1}$ becomes $\frac{1}{4}$.

We can now construct a new equation with the new slope:

$y = \frac{1}{4} x + 2$

That is a perfectly acceptable answer to this question, and to easily generate more equations we can simply change the y intercept to any number we want.

$y = \frac{1}{4} x + 2$
$y = \frac{1}{4} x + 10$
$y = \frac{1}{4} x - 6$