Find the Slope of the Perpendicular Line to the Line Through the Two Points (0,3) , (2,4)

$(0, 3)$ , $(2, 4)$

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.

$m = \frac{4 - (3)}{2 - (0)}$

Step 4

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{4 - 3}{2 - (0)}$

Subtract $3$ from $4$ .

$m = \frac{1}{2 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{1}{2 + 0}$

Add $2$ and $0$ .

$m = \frac{1}{2}$

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 $- \frac{1}{\frac{1}{2}}$ .

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 2)$

Multiply $- (1 \cdot 2)$ .

Multiply $2$ by $1$ .

$m_{perpendicular} = - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$m_{perpendicular} = - 2$

Step 7

Find the Slope of the Perpendicular Line to the Line Through the Two Points (0,3) , (2,4)

Related Questions