# What is the slope of any line perpendicular to the line passing through (15,-12) and (30,34)?

Mar 23, 2018

$\text{slope } = - \frac{15}{46}$

#### Explanation:

$\text{to calculate the slope m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(15,-12)" and } \left({x}_{2} , {y}_{2}\right) = \left(30 , 34\right)$

$\Rightarrow m = \frac{34 - \left(- 12\right)}{30 - 15} = \frac{46}{15}$

$\text{the slope of any line perpendicular to it is }$

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

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{\frac{46}{15}} = - \frac{15}{46}$