Find the Slope of the Perpendicular Line to the Line Through the Two Points (1,0) , (6,8)

$(1, 0)$ , $(6, 8)$

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.

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

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

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

Add $8$ and $0$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{8}{6 - 1}$

Subtract $1$ from $6$ .

$m = \frac{8}{5}$

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 $- \frac{1}{\frac{8}{5}}$ .

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{5}{8}))$

Multiply $\frac{5}{8}$ by $1$ .

$m_{perpendicular} = - \frac{5}{8}$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (1,0) , (6,8)

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