Find the Slope of the Perpendicular Line to the Line Through the Two Points (6,2) , (8,-4)

$(6, 2)$ , $(8, - 4)$

Step 1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 4 - (2)}{8 - (6)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{- 4 - 2}{8 - (6)}$

Subtract $2$ from $- 4$ .

$m = \frac{- 6}{8 - (6)}$

Simplify the denominator.

Multiply $- 1$ by $6$ .

$m = \frac{- 6}{8 - 6}$

Subtract $6$ from $8$ .

$m = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$m = - 3$

Step 5

The slope of a perpendicular line is the negative reciprocal of the slope of the line that passes through the two given points.

$m_{perpendicular} = - \frac{1}{m}$

Step 6

Simplify $- \frac{1}{- 3}$ .

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{3}$

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{3})$

Multiply $\frac{1}{3}$ by $1$ .

$m_{perpendicular} = \frac{1}{3}$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (6,2) , (8,-4)

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