Find the Slope of a Perpendicular Line 2x+y-4=0

$2 x + y - 4 = 0$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Subtract $2 x$ from both sides of the equation.

$y - 4 = - 2 x$

Add $4$ to both sides of the equation.

$y = - 2 x + 4$

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

Step 3

The equation of a perpendicular line to $y = - 2 x + 4$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{2}$

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

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{1}{2})$

Multiply $\frac{1}{2}$ by $1$ .

$m_{perpendicular} = \frac{1}{2}$

Step 5