Find the Slope of a Perpendicular Line 8x+9y=6y-2

$8 x + 9 y = 6 y - 2$

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 containing $y$ to the left side of the equation.

Subtract $6 y$ from both sides of the equation.

$8 x + 9 y - 6 y = - 2$

Subtract $6 y$ from $9 y$ .

$8 x + 3 y = - 2$

Subtract $8 x$ from both sides of the equation.

$3 y = - 2 - 8 x$

Divide each term in $3 y = - 2 - 8 x$ by $3$ and simplify.

Divide each term in $3 y = - 2 - 8 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 2}{3} + \frac{- 8 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 2}{3} + \frac{- 8 x}{3}$

Divide $y$ by $1$ .

$y = \frac{- 2}{3} + \frac{- 8 x}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{2}{3} + \frac{- 8 x}{3}$

Move the negative in front of the fraction.

$y = - \frac{2}{3} - \frac{8 x}{3}$

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

Reorder $- \frac{2}{3}$ and $- \frac{8 x}{3}$ .

$y = - \frac{8 x}{3} - \frac{2}{3}$

Reorder terms.

$y = - (\frac{8}{3} x) - \frac{2}{3}$

Remove parentheses.

$y = - \frac{8}{3} x - \frac{2}{3}$

Step 2

Using the slope-intercept form, the slope is $- \frac{8}{3}$ .

$m = - \frac{8}{3}$

Step 3

The equation of a perpendicular line to $y = - \frac{8}{3} x - \frac{2}{3}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{8}{3}}$

Step 4

Simplify the result.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{8}{3}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{8}{3}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{3}{8})$

Multiply $\frac{3}{8}$ by $1$ .

$m_{perpendicular} = \frac{3}{8}$

Multiply $- - \frac{3}{8}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{3}{8})$

Multiply $\frac{3}{8}$ by $1$ .

$m_{perpendicular} = \frac{3}{8}$

Step 5

Find the Slope of a Perpendicular Line 8x+9y=6y-2

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