Find the Slope of the Perpendicular Line to the Line Through the Two Points (-7,5) , (1,19)

$(- 7, 5)$ , $(1, 19)$

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.

$m = \frac{19 - (5)}{1 - (- 7)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{19 - 5}{1 - (- 7)}$

Subtract $5$ from $19$ .

$m = \frac{14}{1 - (- 7)}$

Simplify the denominator.

Multiply $- 1$ by $- 7$ .

$m = \frac{14}{1 + 7}$

Add $1$ and $7$ .

$m = \frac{14}{8}$

Cancel the common factor of $14$ and $8$ .

Factor $2$ out of $14$ .

$m = \frac{2 (7)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$m = \frac{2 \cdot 7}{2 \cdot 4}$

Cancel the common factor.

$m = \frac{2 \cdot 7}{2 \cdot 4}$

Rewrite the expression.

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

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 $- \frac{1}{\frac{7}{4}}$ .

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{4}{7}))$

Multiply $\frac{4}{7}$ by $1$ .

$m_{perpendicular} = - \frac{4}{7}$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (-7,5) , (1,19)

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