# What is the slope of any line perpendicular to the line passing through (12,-2) and (7,8)?

##### 1 Answer
Mar 28, 2016

$m = \frac{1}{2}$

#### Explanation:

The slope a line that is perpendicular to a given line would be the inverse slope of the given line

$m = \frac{a}{b}$ the perpendicular slope would be $m = - \frac{b}{a}$

The formula for the slope of a line based upon two coordinate points is

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

For the coordinate points $\left(12 , - 2\right) \mathmr{and} \left(7 , 8\right)$
${x}_{1} = 12$
${x}_{2} = 7$
${y}_{1} = - 2$
${y}_{2} = 8$

$m = \frac{8 - \left(- 2\right)}{7 - 12}$

$m = \frac{10}{-} 5$

The slope is $m = - \frac{10}{5} = - \frac{2}{1}$
the perpendicular slope would be the reciprocal (-1/m)
$m = \frac{1}{2}$