Precalculus Examples

$(- 2, - 4)$ , $(- 8, - 5)$

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.

$m = \frac{- 5 - (- 4)}{- 8 - (- 2)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 4$ .

$m = \frac{- 5 + 4}{- 8 - (- 2)}$

Step 4.1.2

Add $- 5$ and $4$ .

$m = \frac{- 1}{- 8 - (- 2)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 2$ .

$m = \frac{- 1}{- 8 + 2}$

Step 4.2.2

Add $- 8$ and $2$ .

$m = \frac{- 1}{- 6}$

Step 4.3

Dividing two negative values results in a positive value.

$m = \frac{1}{6}$

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 $- \frac{1}{\frac{1}{6}}$ .

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 6)$

Step 6.2

Multiply $- (1 \cdot 6)$ .

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Step 6.2.1

Multiply $6$ by $1$ .

$m_{perpendicular} = - 1 \cdot 6$

Step 6.2.2

Multiply $- 1$ by $6$ .

$m_{perpendicular} = - 6$

Step 7

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