Find the Slope of a Perpendicular Line -3x+4y=9

$- 3 x + 4 y = 9$

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.

$y = m x + b$

Add $3 x$ to both sides of the equation.

$4 y = 9 + 3 x$

Divide each term in $4 y = 9 + 3 x$ by $4$ and simplify.

Divide each term in $4 y = 9 + 3 x$ by $4$ .

$\frac{4 y}{4} = \frac{9}{4} + \frac{3 x}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{9}{4} + \frac{3 x}{4}$

Divide $y$ by $1$ .

$y = \frac{9}{4} + \frac{3 x}{4}$

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

Reorder $\frac{9}{4}$ and $\frac{3 x}{4}$ .

$y = \frac{3 x}{4} + \frac{9}{4}$

Reorder terms.

$y = \frac{3}{4} x + \frac{9}{4}$

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 $y = \frac{3}{4} x + \frac{9}{4}$ 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