# How do you graph the line that passes through (4,-2) perpendicular to the graph 3x-2y=6?

Jun 25, 2018

As below

#### Explanation:

$3 x - 2 y = 6$

$2 y = 3 x - 6$

$y = \left(\frac{3}{2}\right) x - 6$

Slope of the line $= m = \frac{3}{2}$

Slope of perpendicular line $= - \frac{1}{m} = - \frac{2}{3}$

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

Equation of the perpendicular line passing through point $\left(4 , - 2\right)$ is

$\left(y + 2\right) = \left(- \frac{2}{3}\right) \left(x - 4\right)$

$3 y + 6 = - 2 x + 8$

$2 x + 3 y = 2$

Let $x = 0 , y = \frac{2}{3}$

Let $x = 1 , y = 0$

Now we know two ordered pairs.

We can plot it on a graph sheet and join the points to form the line.