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

$3 x + y = 15$

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.

$y = 15 - 3 x$

Reorder $15$ and $- 3 x$ .

$y = - 3 x + 15$

Step 2

Using the slope-intercept form, the slope is $- 3$ .

$m = - 3$

Step 3

The equation of a perpendicular line to $y = - 3 x + 15$ must have a slope that is the negative reciprocal of the original slope.

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

Step 4

Simplify the result.

Move the negative in front of the fraction.

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

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

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

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

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

Step 5