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

May 28, 2017

$y = - x + 4$

#### Explanation:

We have been given one point $\left(0 , 4\right)$ and (indirectly) the slope.

It lines are perpendicular, then one slope is the negative reciprocal of the other.

In $y = x$, it is actually $y = + 1 x \text{ }$ so the slope, $m = 1$
The slope perpendicular to this will be $m = - 1$

The point we have been given is a specific point:

It is the $y$-intercept, $c = 4$, so we have everything we need to write the equation of the line in the form $y = m c + c$

$y = - x + 4$