How do you write an equation of a line passing through (6, 3), perpendicular to y = 2x + 2?

Jun 20, 2016

$x + 2 y = 12$

Explanation:

$y = \textcolor{g r e e n}{2} x + 2$ is an equation in slope-intercept form with a slope of $\textcolor{g r e e n}{m = 2}$

All lines perpendicular to $y = \textcolor{g r e e n}{2} x + 2$ will have a slope
$\textcolor{w h i t e}{\text{XXX}} - \frac{1}{\textcolor{g r e e n}{m}} = \textcolor{red}{- \frac{1}{2}}$

If a line has a slope of color(red)(""(-1/2)) and passes through color(blue)(""(6,3))
then we can write its equation in slope-point form as
$\textcolor{w h i t e}{\text{XXX")y-color(blue)(3)=color(red)(} \left(- \frac{1}{2}\right)} \left(x - \textcolor{b l u e}{6}\right)$

While this is a valid answer, we would normally rearrange it into a simpler form:
$\textcolor{w h i t e}{\text{XXX}} 2 y - 6 = 6 - x$
or
$\textcolor{w h i t e}{\text{XXX}} x + 2 y = 12$