Find the Slope of a Perpendicular Line x-9y-5=0

$x - 9 y - 5 = 0$

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 not containing $y$ to the right side of the equation.

Subtract $x$ from both sides of the equation.

$- 9 y - 5 = - x$

Add $5$ to both sides of the equation.

$- 9 y = - x + 5$

Divide each term in $- 9 y = - x + 5$ by $- 9$ and simplify.

Divide each term in $- 9 y = - x + 5$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- x}{- 9} + \frac{5}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- x}{- 9} + \frac{5}{- 9}$

Divide $y$ by $1$ .

$y = \frac{- x}{- 9} + \frac{5}{- 9}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{x}{9} + \frac{5}{- 9}$

Move the negative in front of the fraction.

$y = \frac{x}{9} - \frac{5}{9}$

Reorder terms.

$y = \frac{1}{9} x - \frac{5}{9}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{9}$ .

$m = \frac{1}{9}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{9} x - \frac{5}{9}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 9)$

Multiply $- (1 \cdot 9)$ .

Multiply $9$ by $1$ .

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

Multiply $- 1$ by $9$ .

$m_{perpendicular} = - 9$

Step 5