Finite Math Examples

$(- 4, - 3.5)$ , $(- 2, 1.5)$

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.

$m = \frac{1.5 - (- 3.5)}{- 2 - (- 4)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 3.5$ .

$m = \frac{1.5 + 3.5}{- 2 - (- 4)}$

Step 4.1.2

Add $1.5$ and $3.5$ .

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 4$ .

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

Step 4.2.2

Add $- 2$ and $4$ .

$m = \frac{5}{2}$

Step 4.3

Cancel the common factor of $5$ and $2$ .

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Step 4.3.1

Rewrite $5$ as $1 (5)$ .

$m = \frac{1 (5)}{2}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Rewrite $2$ as $1 (2)$ .

$m = \frac{1 \cdot 5}{1 \cdot 2}$

Step 4.3.2.2

Cancel the common factor.

$m = \frac{1 \cdot 5}{1 \cdot 2}$

Step 4.3.2.3

Rewrite the expression.

$m = \frac{5}{2}$

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 $- \frac{1}{\frac{5}{2}}$ .

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{5}))$

Step 6.2

Multiply $\frac{2}{5}$ by $1$ .

$m_{perpendicular} = - \frac{2}{5}$

Step 7