Find the Slope of the Perpendicular Line to the Line Through the Two Points (1,1) , (5,6)

$(1, 1)$ , $(5, 6)$

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

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).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{6 - (1)}{5 - (1)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $1$ .

$m = \frac{6 - 1}{5 - (1)}$

Subtract $1$ from $6$ .

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

Simplify the denominator.

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Multiply $- 1$ by $1$ .

$m = \frac{5}{5 - 1}$

Subtract $1$ from $5$ .

$m = \frac{5}{4}$

The slope of a perpendicular line is the negative reciprocal of the slope of the line that passes through the two given points.

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

Simplify $- \frac{1}{\frac{5}{4}}$ .

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Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{4}{5}))$

Multiply $\frac{4}{5}$ by $1$ .

$m_{perpendicular} = - \frac{4}{5}$

Find the Slope of the Perpendicular Line to the Line Through the Two Points (1,1) , (5,6)

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