# How do you find an equation of a line containing the point (3, 2), and perpendicular to the line y - 2 = (2/3)x?

May 21, 2016

$y = - \frac{3}{2} x + \frac{13}{2}$

#### Explanation:

Given -

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

Rewrite it -

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

Its Slope ${m}_{1} = \frac{2}{3}$

Two lines are perpendicular if -

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

Find the slope of the perpendicular line

$\frac{2}{3} \times {m}_{2} = - 1$
${m}_{2} = - 1 \times \frac{3}{2} = - \frac{3}{2}$

The perpendicular line is passing through the point $\left(3 , 2\right)$

Its equation is -

$y - {y}_{1} = m 2 \left(x - {x}_{1}\right)$
$y - 2 = - \frac{3}{2} \left(x - 3\right)$
$y = - \frac{3}{2} x + \frac{9}{2} + 2$
$y = - \frac{3}{2} x + \frac{13}{2}$