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

$2 y = 3 x - 1$

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.

$y = m x + b$

Divide each term in $2 y = 3 x - 1$ by $2$ and simplify.

Divide each term in $2 y = 3 x - 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{3}{2}$ .

$m = \frac{3}{2}$

Step 3

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

$m_{perpendicular} = - \frac{1}{\frac{3}{2}}$

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 (\frac{2}{3}))$

Multiply $\frac{2}{3}$ by $1$ .

$m_{perpendicular} = - \frac{2}{3}$

Step 5