Pre-Algebra Examples

$(- 7, - 7)$ , $(- 3, 6)$

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.

$m = \frac{6 - (- 7)}{- 3 - (- 7)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $- 1$ by $- 7$ .

$m = \frac{6 + 7}{- 3 - (- 7)}$

Step 4.1.2

Add $6$ and $7$ .

$m = \frac{13}{- 3 - (- 7)}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 7$ .

$m = \frac{13}{- 3 + 7}$

Step 4.2.2

Add $- 3$ and $7$ .

$m = \frac{13}{4}$

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 $- \frac{1}{\frac{13}{4}}$ .

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{4}{13}))$

Step 6.2

Multiply $\frac{4}{13}$ by $1$ .

$m_{perpendicular} = - \frac{4}{13}$

Step 7