# Given the line 2x - 3y - 5 = 0, how do you find the slope of a line that is perpendicular to this line?

Jun 15, 2018

$- \frac{3}{2}$

#### Explanation:

$2 x - 3 y - 5 = 0$

first rearrange to the form

$y = m x + c$

$2 x - 5 = 3 y$

$\therefore y = \frac{2}{3} x - \frac{5}{3}$

now $m = \text{ the slope/grdient}$

$\implies m = \frac{2}{3}$

for teh perpendicular slope we use teh relation

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

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