Finite Math Examples

$(4, 1)$ , $(- 4, - 5)$

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.

$m = \frac{- 5 - (1)}{- 4 - (4)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $1$ .

$m = \frac{- 5 - 1}{- 4 - (4)}$

Step 4.1.2

Subtract $1$ from $- 5$ .

$m = \frac{- 6}{- 4 - (4)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $4$ .

$m = \frac{- 6}{- 4 - 4}$

Step 4.2.2

Subtract $4$ from $- 4$ .

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

Step 4.3

Cancel the common factor of $- 6$ and $- 8$ .

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Step 4.3.1

Factor $- 2$ out of $- 6$ .

$m = \frac{- 2 \cdot 3}{- 8}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $- 2$ out of $- 8$ .

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

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.

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

Step 6

Simplify $- \frac{1}{\frac{3}{4}}$ .

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{4}{3}))$

Step 6.2

Multiply $\frac{4}{3}$ by $1$ .

$m_{perpendicular} = - \frac{4}{3}$

Step 7