# What is the slope of any line perpendicular to the line passing through (8,12) and (5,-2)?

Feb 16, 2016

The slope $= - \frac{3}{14}$

#### Explanation:

Consider the points :
(x_1, y_1) = color(blue)((8,12)
(x_2, y_2) = color(blue)((5,-2)

The slope joining the pair of points is calculated as :

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

$= \frac{- 2 - 12}{5 - 8}$

$= \frac{- 14}{- 3}$

$= \frac{14}{3}$

The product of slopes of two lines perpendicular to each other is $- 1$.

Hence slope of line perpendicular to the line passing through $\left(8 , 12\right)$ and $\left(5 , - 2\right)$ will be $- \frac{1}{\frac{14}{3}}$ or $- \frac{3}{14}$.