# What is the slope of any line perpendicular to the line passing through (14,2) and (9,5)?

Dec 30, 2015

The slope of the perpendicular is $\frac{5}{3}$ The explanation is given below.

#### Explanation:

Slope $m$ of any line passing through two given points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

The slope of perpendicular would be negative reciprocal of this slope.

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

Our given points are $\left(14 , 2\right)$ and $\left(9 , 5\right)$

${x}_{1} = 14$, ${y}_{1} = 2$
${x}_{2} = 9$, ${y}_{2} = 5$

The slope of any line perpendicular to the line joining $\left(14 , 2\right)$ and $\left(9.5\right)$ is given by.

${m}_{p} = - \frac{9 - 14}{5 - 2}$
${m}_{p} = - \frac{- 5}{3}$
${m}_{p} = \frac{5}{3}$

The slope of the perpendicular is $\frac{5}{3}$