Find the Slope of the Perpendicular Line to the Line Through the Two Points (15,9) , (12,-7)

$(15, 9)$ , $(12, - 7)$

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.

$m = \frac{- 7 - (9)}{12 - (15)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $9$ .

$m = \frac{- 7 - 9}{12 - (15)}$

Subtract $9$ from $- 7$ .

$m = \frac{- 16}{12 - (15)}$

Simplify the denominator.

Multiply $- 1$ by $15$ .

$m = \frac{- 16}{12 - 15}$

Subtract $15$ from $12$ .

$m = \frac{- 16}{- 3}$

Dividing two negative values results in a positive value.

$m = \frac{16}{3}$

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 $- \frac{1}{\frac{16}{3}}$ .

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{3}{16}))$

Multiply $\frac{3}{16}$ by $1$ .

$m_{perpendicular} = - \frac{3}{16}$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (15,9) , (12,-7)

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