Find the Slope of a Perpendicular Line (y-1)=1/3x

$(y - 1) = \frac{1}{3} x$

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.

$y = m x + b$

Simplify the right side.

Combine $\frac{1}{3}$ and $x$ .

$(y - 1) = \frac{x}{3}$

Add $1$ to both sides of the equation.

$y = \frac{x}{3} + 1$

Reorder terms.

$y = \frac{1}{3} x + 1$

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 $y = \frac{1}{3} x + 1$ 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