Find the Slope of the Perpendicular Line to the Line Through the Two Points (3,-3) , (3,-4)

$(3, - 3)$ ,

$(3, - 4)$

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.

$m = \frac{- 4 - (- 3)}{3 - (3)}$

Step 4

Simplify.

Multiply

$- 1$ by

$3$ .

$\frac{- 4 - (- 3)}{3 - 3}$

Subtract

$3$ from

$3$ .

$\frac{- 4 - (- 3)}{0}$

The expression contains a division by

$0$ . The expression is undefined.

Undefined

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

The slope of a line perpendicular to a vertical line is zero.

$m_{perpendicular} = 0$

Step 7