# What is the slope of any line perpendicular to the line passing through (30,32) and (18,40)?

Oct 7, 2016

$\text{slope of any line : } m = \frac{3}{2}$

#### Explanation:

$\text{draw the line passing through (30,32) and (18,40)}$

${m}_{1} : \text{slope of the blue line}$

$m : \text{slope of the red line}$

$\text{find slope of the blue line}$

$\tan \alpha = \frac{32 - 40}{30 - 18}$

$\tan \alpha = - \frac{8}{12} = - \frac{2}{3}$

${m}_{1} \cdot m = - 1$

$- \frac{2}{3} \cdot m = - 1$

$- 2 m = - 3$

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