Precalculus Examples

(- 2, - 4)

$(- 2, - 4)$ ,

(- 8, - 5)

$(- 8, - 5)$

Step 1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{change in y}{change in x}

$m = \frac{change in y}{change in x}$

Step 2

The change in

x

$x$ is equal to the difference in x-coordinates (also called run), and the change in

y

$y$ is equal to the difference in y-coordinates (also called rise).

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

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

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply

- 1

$- 1$ by

- 4

$- 4$ .

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

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

Step 4.1.2

Add

- 5

$- 5$ and

4

$4$ .

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

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

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

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

- 2

$- 2$ .

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

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

Step 4.2.2

Add

- 8

$- 8$ and

2

$2$ .

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

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

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

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

Step 4.3

Dividing two negative values results in a positive value.

m = \frac{1}{6}

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

m = \frac{1}{6}

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

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}

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

Step 6

Simplify

- \frac{1}{\frac{1}{6}}

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

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 6.2

Multiply

- (1 \cdot 6)

$- (1 \cdot 6)$ .

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Step 6.2.1

Multiply

6

$6$ by

1

$1$ .

m_{perpendicular} = - 1 \cdot 6

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

Step 6.2.2

Multiply

- 1

$- 1$ by

6

$6$ .

m_{perpendicular} = - 6

$m_{perpendicular} = - 6$

m_{perpendicular} = - 6

$m_{perpendicular} = - 6$

m_{perpendicular} = - 6

$m_{perpendicular} = - 6$

Step 7

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