# How do you find the slope of a line perpendicular to the line to the line through the points (7,-10) and (6,-1)?

May 14, 2018

The perpendicular slope would be $m = \frac{1}{9}$

#### Explanation:

Let's begin by finding the slope of the line through the two points, $\left(7 , - 10\right)$ and $\left(6 , - 1\right)$

Slope is The change in $y$ rise over the change in $x$ run.

$m = \frac{\Delta y}{\Delta x}$

and can be found using the equation

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

For the points given the coordinates are

${x}_{1} = 7$
${y}_{1} = - 10$
${x}_{2} = 6$
${y}_{2} = - 1$

Plug in the values and solve for slope

$m = \frac{- 1 - \left(- 10\right)}{6 - 7}$

$m = \frac{9}{-} 1$

$m = - 9$

The line perpendicular to this line would have a slope that is the inverse of this line. Both in sign and reciprocal.

#m - 1/9