Find the Slope of a Perpendicular Line 3x-9y=15

$3 x - 9 y = 15$

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.

$- 9 y = 15 - 3 x$

Divide each term in $- 9 y = 15 - 3 x$ by $- 9$ and simplify.

Divide each term in $- 9 y = 15 - 3 x$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{15}{- 9} + \frac{- 3 x}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{15}{- 9} + \frac{- 3 x}{- 9}$

Divide $y$ by $1$ .

$y = \frac{15}{- 9} + \frac{- 3 x}{- 9}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $15$ and $- 9$ .

Factor $3$ out of $15$ .

$y = \frac{3 (5)}{- 9} + \frac{- 3 x}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$y = \frac{3 \cdot 5}{3 \cdot - 3} + \frac{- 3 x}{- 9}$

Cancel the common factor.

$y = \frac{3 \cdot 5}{3 \cdot - 3} + \frac{- 3 x}{- 9}$

Rewrite the expression.

$y = \frac{5}{- 3} + \frac{- 3 x}{- 9}$

Move the negative in front of the fraction.

$y = - \frac{5}{3} + \frac{- 3 x}{- 9}$

Cancel the common factor of $- 3$ and $- 9$ .

Factor $- 3$ out of $- 3 x$ .

$y = - \frac{5}{3} + \frac{- 3 (x)}{- 9}$

Cancel the common factors.

Factor $- 3$ out of $- 9$ .

$y = - \frac{5}{3} + \frac{- 3 (x)}{- 3 (3)}$

Cancel the common factor.

$y = - \frac{5}{3} + \frac{- 3 x}{- 3 \cdot 3}$

Rewrite the expression.

$y = - \frac{5}{3} + \frac{x}{3}$

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

Reorder $- \frac{5}{3}$ and $\frac{x}{3}$ .

$y = \frac{x}{3} - \frac{5}{3}$

Reorder terms.

$y = \frac{1}{3} x - \frac{5}{3}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{3}$ .

$m = \frac{1}{3}$

Step 3

The equation of a perpendicular line to $y = \frac{1}{3} x - \frac{5}{3}$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Multiply the numerator by the reciprocal of the denominator.

$m_{perpendicular} = - (1 \cdot 3)$

Multiply $- (1 \cdot 3)$ .

Multiply $3$ by $1$ .

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

Multiply $- 1$ by $3$ .

$m_{perpendicular} = - 3$

Step 5

Find the Slope of a Perpendicular Line 3x-9y=15

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