Write in Slope-Intercept Form y-3=-1/3(x-1)

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

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

Simplify the right side.

Simplify $- \frac{1}{3} (x - 1)$ .

Apply the distributive property.

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

Move all terms not containing $y$ to the right side of the equation.

Add $3$ to both sides of the equation.

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$y = - \frac{x}{3} + \frac{1 + 9}{3}$

Add $1$ and $9$ .

$y = - \frac{x}{3} + \frac{10}{3}$

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

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{10}{3}$

Remove parentheses.

$y = - \frac{1}{3} x + \frac{10}{3}$