Find the Slope of the Perpendicular Line to the Line Through the Two Points (-7,2) , (9,6)

$(- 7, 2)$ , $(9, 6)$

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.

$m = \frac{6 - (2)}{9 - (- 7)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{6 - 2}{9 - (- 7)}$

Subtract $2$ from $6$ .

$m = \frac{4}{9 - (- 7)}$

Simplify the denominator.

Multiply $- 1$ by $- 7$ .

$m = \frac{4}{9 + 7}$

Add $9$ and $7$ .

$m = \frac{4}{16}$

Cancel the common factor of $4$ and $16$ .

Factor $4$ out of $4$ .

$m = \frac{4 (1)}{16}$

Cancel the common factors.

Factor $4$ out of $16$ .

$m = \frac{4 \cdot 1}{4 \cdot 4}$

Cancel the common factor.

$m = \frac{4 \cdot 1}{4 \cdot 4}$

Rewrite the expression.

$m = \frac{1}{4}$

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 $- \frac{1}{\frac{1}{4}}$ .

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 4)$

Multiply $- (1 \cdot 4)$ .

Multiply $4$ by $1$ .

$m_{perpendicular} = - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$m_{perpendicular} = - 4$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (-7,2) , (9,6)

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