# What is the slope of any line perpendicular to the line passing through (-2,6) and (-7,4)?

Apr 29, 2016

Slope of the perpendicular line ${m}_{2} = - \frac{5}{2}$

#### Explanation:

Given -

The two points on the given line.

${x}_{1} = - 2$
${y}_{1} = 6$
${x}_{2} = - 7$
${y}_{2} = 4$

Slope of the given line ${m}_{1}$

$= \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 - 6}{- 7 - \left(- 2\right)} = \frac{- 2}{- 5} = \frac{2}{5}$

Slope of the perpendicular line ${m}_{2}$

Two line are perpendicular if $\left({m}_{1} \times {m}_{2} = - 1\right)$

Find ${m}_{2}$

$\frac{2}{5} \times {m}_{2} = - 1$
${m}_{2} = - 1 \times \frac{5}{2} = - \frac{5}{2}$

Apr 29, 2016

$- \frac{5}{2}$
Find slope of line through points using formula $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. Slope of a line perpendicular to a given line is the negative reciprocal.