# How do you write the equation in slope intercept form perpendicular to the line 2x -3y = 12 and passes through the point (2, 6)?

Apr 26, 2018

$y = - \frac{3}{2} x + 9$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{rearrange "2x-3y=12" into this form}$

$\text{subtract 2x from both sides}$

$\Rightarrow - 3 y = - 2 x + 12$

$\text{divide all terms by } - 3$

$\Rightarrow y = \frac{2}{3} x - 4 \leftarrow \textcolor{b l u e}{\text{in standard form}}$

$\text{with } m = \frac{2}{3}$

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{\frac{2}{3}} = - \frac{3}{2}$

$\Rightarrow y = - \frac{3}{2} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(2,6)" into the partial equation}$

$6 = - 3 + b \Rightarrow b = 6 + 3 = 9$

$\Rightarrow y = - \frac{3}{2} x + 9 \leftarrow \textcolor{red}{\text{equation of perpendicular line}}$