# What is the equation of the line that is perpendicular to the line -3x + y = -2 and contains the point (3,6)?

Sep 20, 2017

$3 y + x = 21$

#### Explanation:

Use

$y = m x + c$

where $m$ is the slope

$- 3 x + y = - 2$

$y = 3 y - 2$

So

$m = 3$

The slope of the perpendicular line is $- \frac{1}{3}$ as

${m}_{1} \cdot {m}_{2} = - 1$

The equation of the perpendicular line is

$\left(y - {y}_{1}\right) = {m}_{2} \left(x - {x}_{1}\right)$

where ${m}_{2}$ is the slope of the perpendicular line $= - \frac{1}{3}$ and ${x}_{1}$ and ${y}_{1}$ are the $x$ and $y$ coordinates of a point on it.

$y - 6 = - \frac{1}{3} \cdot \left(x - 3\right)$

$3 y - 18 = - x + 3$

$3 y + x = 21$

is the equation of the perpendicular line.