Finite Math Examples

(6, 3)

$(6, 3)$ ,

(- 8, 8)

$(- 8, 8)$

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{8 - (3)}{- 8 - (6)}

$m = \frac{8 - (3)}{- 8 - (6)}$

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

3

$3$ .

m = \frac{8 - 3}{- 8 - (6)}

$m = \frac{8 - 3}{- 8 - (6)}$

Step 4.1.2

Subtract

3

$3$ from

8

$8$ .

m = \frac{5}{- 8 - (6)}

$m = \frac{5}{- 8 - (6)}$

m = \frac{5}{- 8 - (6)}

$m = \frac{5}{- 8 - (6)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply

- 1

$- 1$ by

6

$6$ .

m = \frac{5}{- 8 - 6}

$m = \frac{5}{- 8 - 6}$

Step 4.2.2

Subtract

6

$6$ from

- 8

$- 8$ .

m = \frac{5}{- 14}

$m = \frac{5}{- 14}$

m = \frac{5}{- 14}

$m = \frac{5}{- 14}$

Step 4.3

Move the negative in front of the fraction.

m = - \frac{5}{14}

$m = - \frac{5}{14}$

m = - \frac{5}{14}

$m = - \frac{5}{14}$

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{5}{14}}

$- \frac{1}{- \frac{5}{14}}$ .

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Step 6.1

Cancel the common factor of

1

$1$ and

- 1

$- 1$ .

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Step 6.1.1

Rewrite

1

$1$ as

- 1 (- 1)

$- 1 (- 1)$ .

m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{5}{14}}

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{5}{14}}$

Step 6.1.2

Move the negative in front of the fraction.

m_{perpendicular} = \frac{1}{\frac{5}{14}}

$m_{perpendicular} = \frac{1}{\frac{5}{14}}$

m_{perpendicular} = \frac{1}{\frac{5}{14}}

$m_{perpendicular} = \frac{1}{\frac{5}{14}}$

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

m_{perpendicular} = 1 (\frac{14}{5})

$m_{perpendicular} = 1 (\frac{14}{5})$

Step 6.3

Multiply

\frac{14}{5}

$\frac{14}{5}$ by

1

$1$ .

m_{perpendicular} = \frac{14}{5}

$m_{perpendicular} = \frac{14}{5}$

Step 6.4

Multiply

- - \frac{14}{5}

$- - \frac{14}{5}$ .

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Step 6.4.1

Multiply

- 1

$- 1$ by

- 1

$- 1$ .

m_{perpendicular} = 1 (\frac{14}{5})

$m_{perpendicular} = 1 (\frac{14}{5})$

Step 6.4.2

Multiply

\frac{14}{5}

$\frac{14}{5}$ by

1

$1$ .

m_{perpendicular} = \frac{14}{5}

$m_{perpendicular} = \frac{14}{5}$

m_{perpendicular} = \frac{14}{5}

$m_{perpendicular} = \frac{14}{5}$

m_{perpendicular} = \frac{14}{5}

$m_{perpendicular} = \frac{14}{5}$

Step 7