# How do you write an equation in standard form for a line passing through (2, 1) and is perpendicular to x = –2?

May 2, 2015

$x = - 2$ represents a vertical line so that a perpendicular line to it will be a perfectly horizontal line passing through $\left(2 , 1\right)$.
A perfectly horizontal line has slope $m = 0$ (it is not increasing nor decreasing) so you can use your relationship:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$ with $m = 0$ giving:
$y - 1 = 0 \left(x - 2\right)$
So your line has equation: $\textcolor{red}{y = 1}$