Find the Slope of a Perpendicular Line y=3/4x-1/2

$y = \frac{3}{4} x - \frac{1}{2}$

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.

$y = m x + b$

Simplify the right side.

Combine $\frac{3}{4}$ and $x$ .

$y = \frac{3 x}{4} - \frac{1}{2}$

Reorder terms.

$y = \frac{3}{4} x - \frac{1}{2}$

Using the slope-intercept form, the slope is $\frac{3}{4}$ .

$m = \frac{3}{4}$

The equation of a perpendicular line to $y = \frac{3}{4} x - \frac{1}{2}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{\frac{3}{4}}$

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{4}{3}))$

Multiply $\frac{4}{3}$ by $1$ .

$m_{perpendicular} = - \frac{4}{3}$