Find the Slope of the Perpendicular Line to the Line Through the Two Points (-11.3,-11.6) , (12.8,4.5)

$(- 11.3, - 11.6)$ , $(12.8, 4.5)$

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.

$m = \frac{4.5 - (- 11.6)}{12.8 - (- 11.3)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $- 11.6$ .

$m = \frac{4.5 + 11.6}{12.8 - (- 11.3)}$

Add $4.5$ and $11.6$ .

$m = \frac{16.1}{12.8 - (- 11.3)}$

Simplify the denominator.

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Multiply $- 1$ by $- 11.3$ .

$m = \frac{16.1}{12.8 + 11.3}$

Add $12.8$ and $11.3$ .

$m = \frac{16.1}{24.1}$

Divide $16.1$ by $24.1$ .

$m = 0.66804979$

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

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

The slope of the perpendicular line is $- \frac{1}{0.66804979}$ .

$m_{perpendicular} = - \frac{1}{0.66804979}$

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