Precalculus Examples

(2, 7)

$(2, 7)$ ,

(3, 3)

$(3, 3)$

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{3 - (7)}{3 - (2)}

$m = \frac{3 - (7)}{3 - (2)}$

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

7

$7$ .

m = \frac{3 - 7}{3 - (2)}

$m = \frac{3 - 7}{3 - (2)}$

Step 4.1.2

Subtract

7

$7$ from

3

$3$ .

m = \frac{- 4}{3 - (2)}

$m = \frac{- 4}{3 - (2)}$

m = \frac{- 4}{3 - (2)}

$m = \frac{- 4}{3 - (2)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

2

$2$ .

m = \frac{- 4}{3 - 2}

$m = \frac{- 4}{3 - 2}$

Step 4.2.2

Subtract

2

$2$ from

3

$3$ .

m = \frac{- 4}{1}

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

m = \frac{- 4}{1}

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

Step 4.3

Divide

- 4

$- 4$ by

1

$1$ .

m = - 4

$m = - 4$

m = - 4

$m = - 4$

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}

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

Step 6

Simplify

- \frac{1}{- 4}

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

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Step 6.1

Move the negative in front of the fraction.

m_{perpendicular} = \frac{1}{4}

$m_{perpendicular} = \frac{1}{4}$

Step 6.2

Multiply

- - \frac{1}{4}

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

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Step 6.2.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

m_{perpendicular} = 1 (\frac{1}{4})

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

Step 6.2.2

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

1

$1$ .

m_{perpendicular} = \frac{1}{4}

$m_{perpendicular} = \frac{1}{4}$

m_{perpendicular} = \frac{1}{4}

$m_{perpendicular} = \frac{1}{4}$

m_{perpendicular} = \frac{1}{4}

$m_{perpendicular} = \frac{1}{4}$

Step 7

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