# What is the slope any line perpendicular to the line passing through (-8,1) and (-5,12)?

Jun 28, 2017

$- \frac{3}{11}$

#### Explanation:

$\text{given a line with slope m then the slope of any line}$
$\text{perpendicular to it is}$

${m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{m}$

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where " (x_1,y_1),(x_2,y_2)" are 2 coordinate points}$

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(- 8 , 1\right) , \left({x}_{2} , {y}_{2}\right) = \left(- 5 , 12\right)$

$\Rightarrow m = \frac{12 - 1}{- 5 - \left(- 8\right)} = \frac{11}{3}$

$\Rightarrow {m}_{\textcolor{red}{\text{perpendicular}}} = - \frac{1}{\frac{11}{3}} = - \frac{3}{11}$