# What is the slope of any line perpendicular to the line passing through (9,15) and (7,2)?

Apr 10, 2018

$- \frac{2}{13}$

#### Explanation:

Let the slope of the line joining the 2 points be $m$ and the slope of the line perpendicular to it be ${m}_{1}$.

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{15 - 2}{9 - 7} = \frac{13}{2}$

We know, $m {m}_{1} = - 1$

So ${m}_{1} = - \frac{2}{13}$ [ANS]

Apr 10, 2018

$\text{perpendicular slope } = - \frac{2}{13}$

#### Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(9,15)" and } \left({x}_{2} , {y}_{2}\right) = \left(7 , 2\right)$

$\Rightarrow m = \frac{2 - 15}{7 - 9} = \frac{- 13}{- 2} = \frac{13}{2}$

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

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

$\Rightarrow \text{perpendicular slope } = - \frac{1}{\frac{13}{2}} = - \frac{2}{13}$