Find the Slope of a Perpendicular Line 4x+9y=-10

$4 x + 9 y = - 10$

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 $4 x$ from both sides of the equation.

$9 y = - 10 - 4 x$

Divide each term in $9 y = - 10 - 4 x$ by $9$ and simplify.

Divide each term in $9 y = - 10 - 4 x$ by $9$ .

$\frac{9 y}{9} = \frac{- 10}{9} + \frac{- 4 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 10}{9} + \frac{- 4 x}{9}$

Divide $y$ by $1$ .

$y = \frac{- 10}{9} + \frac{- 4 x}{9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{10}{9} + \frac{- 4 x}{9}$

Move the negative in front of the fraction.

$y = - \frac{10}{9} - \frac{4 x}{9}$

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

Reorder $- \frac{10}{9}$ and $- \frac{4 x}{9}$ .

$y = - \frac{4 x}{9} - \frac{10}{9}$

Reorder terms.

$y = - (\frac{4}{9} x) - \frac{10}{9}$

Remove parentheses.

$y = - \frac{4}{9} x - \frac{10}{9}$

Step 2

Using the slope-intercept form, the slope is $- \frac{4}{9}$ .

$m = - \frac{4}{9}$

Step 3

The equation of a perpendicular line to $y = - \frac{4}{9} x - \frac{10}{9}$ must have a slope that is the negative reciprocal of the original slope.

$m_{perpendicular} = - \frac{1}{- \frac{4}{9}}$

Step 4

Simplify the result.

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

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

$m_{perpendicular} = - \frac{- 1 \cdot - 1}{- \frac{4}{9}}$

Move the negative in front of the fraction.

$m_{perpendicular} = \frac{1}{\frac{4}{9}}$

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = 1 (\frac{9}{4})$

Multiply $\frac{9}{4}$ by $1$ .

$m_{perpendicular} = \frac{9}{4}$

Multiply $- - \frac{9}{4}$ .

Multiply $- 1$ by $- 1$ .

$m_{perpendicular} = 1 (\frac{9}{4})$

Multiply $\frac{9}{4}$ by $1$ .

$m_{perpendicular} = \frac{9}{4}$

Step 5

Find the Slope of a Perpendicular Line 4x+9y=-10

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