Finite Math Examples

$(- 4, 6)$ , $(2, 6)$

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.

$m = \frac{6 - (6)}{2 - (- 4)}$

Step 4

Simplify.

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Step 4.1

Reduce the expression by cancelling the common factors.

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Step 4.1.1

Cancel the common factor of $6 - (6)$ and $2 - (- 4)$ .

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Step 4.1.1.1

Rewrite $6$ as $- 1 (- 6)$ .

$m = \frac{- 1 \cdot - 6 - (6)}{2 - (- 4)}$

Step 4.1.1.2

Factor $- 1$ out of $- 1 (- 6) - (6)$ .

$m = \frac{- 1 (- 6 + 6)}{2 - (- 4)}$

Step 4.1.1.3

Reorder terms.

$m = \frac{- 1 (- 6 + 6)}{2 - 4 \cdot - 1}$

Step 4.1.1.4

Factor $2$ out of $- 1 (- 6 + 6)$ .

$m = \frac{2 (- 1 (- 3 + 3))}{2 - 4 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor $2$ out of $2$ .

$m = \frac{2 (- 1 (- 3 + 3))}{2 (1) - 4 \cdot - 1}$

Step 4.1.1.5.2

Factor $2$ out of $- 4 \cdot - 1$ .

$m = \frac{2 (- 1 (- 3 + 3))}{2 (1) + 2 (- 2 \cdot - 1)}$

Step 4.1.1.5.3

Factor $2$ out of $2 (1) + 2 (- 2 \cdot - 1)$ .

$m = \frac{2 (- 1 (- 3 + 3))}{2 (1 - 2 \cdot - 1)}$

Step 4.1.1.5.4

Cancel the common factor.

$m = \frac{2 (- 1 (- 3 + 3))}{2 (1 - 2 \cdot - 1)}$

Step 4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (- 3 + 3)}{1 - 2 \cdot - 1}$

Step 4.1.2

Add $- 3$ and $3$ .

$m = \frac{- 1 \cdot 0}{1 - 2 \cdot - 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 2$ by $- 1$ .

$m = \frac{- 1 \cdot 0}{1 + 2}$

Step 4.2.2

Add $1$ and $2$ .

$m = \frac{- 1 \cdot 0}{3}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $- 1$ by $0$ .

$m = \frac{0}{3}$

Step 4.3.2

Divide $0$ by $3$ .

$m = 0$

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

The slope of the perpendicular line is $- \frac{1}{0}$ .

$m_{perpendicular} = - \frac{1}{0}$

Step 7

The slope of a line perpendicular to a horizontal line is undefined.

Undefined Slope

Step 8