# What is the slope of any line perpendicular to the line passing through (-25,18) and (10,-21)?

Jun 12, 2018

$\text{perpendicular slope } = \frac{35}{39}$

#### Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-25,18)" and } \left({x}_{2} , {y}_{2}\right) = \left(10 , - 21\right)$

$m = \frac{- 21 - 18}{10 - \left(- 25\right)} = \frac{- 39}{35} = - \frac{39}{35}$

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

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

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{- \frac{39}{35}} = \frac{35}{39}$