Find the Slope of a Perpendicular Line 3x-4y=12

$3 x - 4 y = 12$

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.

$y = m x + b$

Subtract $3 x$ from both sides of the equation.

$- 4 y = 12 - 3 x$

Divide each term in $- 4 y = 12 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 12 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 4$ .

$y = - 3 + \frac{- 3 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - 3 + \frac{3 x}{4}$

Write in $y = m x + b$ form.

Reorder $- 3$ and $\frac{3 x}{4}$ .

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

Reorder terms.

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

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

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

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

Step 5