Finite Math Examples

$(2, a)$ , $(5, - 3)$

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.

$m = \frac{- 3 - (a)}{5 - (2)}$

Step 4

Simplify.

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Step 4.1

Simplify the denominator.

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Step 4.1.1

Multiply $- 1$ by $2$ .

$m = \frac{- 3 - a}{5 - 2}$

Step 4.1.2

Subtract $2$ from $5$ .

$m = \frac{- 3 - a}{3}$

Step 4.2

Simplify with factoring out.

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Step 4.2.1

Rewrite $- 3$ as $- 1 (3)$ .

$m = \frac{- 1 \cdot 3 - a}{3}$

Step 4.2.2

Factor $- 1$ out of $- a$ .

$m = \frac{- 1 \cdot 3 - (a)}{3}$

Step 4.2.3

Factor $- 1$ out of $- 1 (3) - (a)$ .

$m = \frac{- 1 (3 + a)}{3}$

Step 4.2.4

Move the negative in front of the fraction.

$m = - \frac{3 + a}{3}$

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 $- \frac{1}{- \frac{3 + a}{3}}$ .

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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 $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{3 + a}{3}}$

Step 6.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{3 + a}{3}}$

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{3}{3 + a})$

Step 6.3

Multiply $\frac{3}{3 + a}$ by $1$ .

$m_{perpendicular} = \frac{3}{3 + a}$

Step 6.4

Multiply $- - \frac{3}{3 + a}$ .

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Step 6.4.1

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{3}{3 + a})$

Step 6.4.2

Multiply $\frac{3}{3 + a}$ by $1$ .

$m_{perpendicular} = \frac{3}{3 + a}$

Step 7