Find the Slope of the Perpendicular Line to the Line Through the Two Points (-4,-8) , (0,0)

$(- 4, - 8)$ , $(0, 0)$

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.

$m = \frac{0 - (- 8)}{0 - (- 4)}$

Step 4

Simplify.

Reduce the expression by cancelling the common factors.

Cancel the common factor of $0 - (- 8)$ and $0 - (- 4)$ .

Rewrite $0$ as $- 1 (0)$ .

$m = \frac{- 1 \cdot 0 - (- 8)}{0 - (- 4)}$

Factor $- 1$ out of $- 1 (0) - (- 8)$ .

$m = \frac{- 1 (0 - 8)}{0 - (- 4)}$

Reorder terms.

$m = \frac{- 1 (0 - 8)}{0 - 4 \cdot - 1}$

Factor $4$ out of $- 1 (0 - 8)$ .

$m = \frac{4 (- 1 (0 - 2))}{0 - 4 \cdot - 1}$

Cancel the common factors.

Factor $4$ out of $0$ .

$m = \frac{4 (- 1 (0 - 2))}{4 (0) - 4 \cdot - 1}$

Factor $4$ out of $- 4 \cdot - 1$ .

$m = \frac{4 (- 1 (0 - 2))}{4 (0) + 4 (1)}$

Factor $4$ out of $4 (0) + 4 (- - 1)$ .

$m = \frac{4 (- 1 (0 - 2))}{4 (0 + 1)}$

Cancel the common factor.

$m = \frac{4 (- 1 (0 - 2))}{4 (0 + 1)}$

Rewrite the expression.

$m = \frac{- 1 (0 - 2)}{0 + 1}$

Subtract $2$ from $0$ .

$m = \frac{- 1 \cdot - 2}{0 + 1}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot - 2}{0 + 1}$

Add $0$ and $1$ .

$m = \frac{- 1 \cdot - 2}{1}$

Simplify the expression.

Multiply $- 1$ by $- 2$ .

$m = \frac{2}{1}$

Divide $2$ by $1$ .

$m = 2$

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

The slope of the perpendicular line is $- \frac{1}{2}$ .

$m_{perpendicular} = - \frac{1}{2}$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (-4,-8) , (0,0)

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