Finite Math Examples

$(6, 3)$ , $(- 8, 8)$

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.

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

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $3$ .

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

Step 4.1.2

Subtract $3$ from $8$ .

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $6$ .

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

Step 4.2.2

Subtract $6$ from $- 8$ .

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

Step 4.3

Move the negative in front of the fraction.

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

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.

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

Step 6

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

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Step 6.1

Cancel the common factor of $1$ and $- 1$ .

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Step 6.1.1

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

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

Step 6.1.2

Move the negative in front of the fraction.

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

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 6.3

Multiply $\frac{14}{5}$ by $1$ .

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

Step 6.4

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

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Step 6.4.1

Multiply $- 1$ by $- 1$ .

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

Step 6.4.2

Multiply $\frac{14}{5}$ by $1$ .

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

Step 7