# How do you the equation of the line that is perpendicular to the line 2x - 3y = 3 and passes through the point (-8, 2)?

May 26, 2017

When given a line in form $a x - b y = c$, the equation of all lines that are perpendicular are of the form:

$b x + a y = k$

Use the given point to find the value of $k$

#### Explanation:

The equation of all lines that are perpendicular are:

$3 x + 2 y = k$

To find the value of k, substitute the point $\left(- 8 , 2\right)$

$3 \left(- 8\right) + 2 \left(2\right) = k$

$- 24 + 4 = k$

$k = - 20$

The equation of the line perpendicular to $2 x - 3 y = 3$ that passes through the point $\left(- 8 , 2\right)$ is:

$3 x + 2 y = - 20$