Finite Math Examples

$(- 48, 0)$ , $(0, - 8)$

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.

$m = \frac{- 8 - (0)}{0 - (- 48)}$

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 $- 8 - (0)$ and $0 - (- 48)$ .

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Step 4.1.1.1

Rewrite $- 8$ as $- 1 (8)$ .

$m = \frac{- 1 \cdot 8 - (0)}{0 - (- 48)}$

Step 4.1.1.2

Factor $- 1$ out of $- 1 (8) - (0)$ .

$m = \frac{- 1 (8 + 0)}{0 - (- 48)}$

Step 4.1.1.3

Reorder terms.

$m = \frac{- 1 (8 + 0)}{0 - 48 \cdot - 1}$

Step 4.1.1.4

Factor $8$ out of $- 1 (8 + 0)$ .

$m = \frac{8 (- 1 (1 + 0))}{0 - 48 \cdot - 1}$

Step 4.1.1.5

Cancel the common factors.

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Step 4.1.1.5.1

Factor $8$ out of $0$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0) - 48 \cdot - 1}$

Step 4.1.1.5.2

Factor $8$ out of $- 48 \cdot - 1$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0) + 8 (- 6 \cdot - 1)}$

Step 4.1.1.5.3

Factor $8$ out of $8 (0) + 8 (- 6 \cdot - 1)$ .

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 4.1.1.5.4

Cancel the common factor.

$m = \frac{8 (- 1 (1 + 0))}{8 (0 - 6 \cdot - 1)}$

Step 4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 0)}{0 - 6 \cdot - 1}$

Step 4.1.2

Add $1$ and $0$ .

$m = \frac{- 1 \cdot 1}{0 - 6 \cdot - 1}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 6$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 6}$

Step 4.2.2

Add $0$ and $6$ .

$m = \frac{- 1 \cdot 1}{6}$

Step 4.3

Simplify the expression.

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Step 4.3.1

Multiply $- 1$ by $1$ .

$m = \frac{- 1}{6}$

Step 4.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{6}$

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 $- \frac{1}{- \frac{1}{6}}$ .

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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 $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{1}{6}}$

Step 6.1.2

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{1}{6}}$

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 \cdot 6$

Step 6.3

Multiply $- - (1 \cdot 6)$ .

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Step 6.3.1

Multiply $6$ by $1$ .

$m_{perpendicular} = - (- 1 \cdot 6)$

Step 6.3.2

Multiply $- 1$ by $6$ .

$m_{perpendicular} = 6$

Step 6.3.3

Multiply $- 1$ by $- 6$ .

$m_{perpendicular} = 6$

Step 7