Find the Slope of a Perpendicular Line 3x+8y=9

$3 x + 8 y = 9$

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.

$y = m x + b$

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

$8 y = 9 - 3 x$

Divide each term in $8 y = 9 - 3 x$ by $8$ and simplify.

Divide each term in $8 y = 9 - 3 x$ by $8$ .

$\frac{8 y}{8} = \frac{9}{8} + \frac{- 3 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{9}{8} + \frac{- 3 x}{8}$

Divide $y$ by $1$ .

$y = \frac{9}{8} + \frac{- 3 x}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{9}{8} - \frac{3 x}{8}$

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

Reorder $\frac{9}{8}$ and $- \frac{3 x}{8}$ .

$y = - \frac{3 x}{8} + \frac{9}{8}$

Reorder terms.

$y = - (\frac{3}{8} x) + \frac{9}{8}$

Remove parentheses.

$y = - \frac{3}{8} x + \frac{9}{8}$

Step 2

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

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

Step 3

The equation of a perpendicular line to $y = - \frac{3}{8} x + \frac{9}{8}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

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

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

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

Move the negative in front of the fraction.

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

Step 5

Find the Slope of a Perpendicular Line 3x+8y=9

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