# How do you write the equation of the line that is perpendicular to the line 3x - 2y = 6 and passes through the point (-1,2)?

Apr 29, 2017

When given a line of the standard form:
$a x + b y = c$
Swap "a" and "b":
$b x + a y = c$
Then change the sign of "a" or "b":
$- b x + a y = c$ or $b x - a y = c$
Find a new value for "c" by substituting in the given point.

#### Explanation:

Given:

$3 x - 2 y = 6$

Swap "a" and "b":

$- 2 x + 3 y = 6$

We shall change the sign of -2:

$2 x + 3 y = 6$

Determine a new value for c by substituting in the point, $\left(- 1 , 2\right)$:

$2 \left(- 1\right) + 3 \left(2\right) = 4$

The equation of the desired line is:

$2 x + 3 y = 4$

Here is a graph of the two lines and the point: