Write in y=mx+b Form 1/2x+1/3y=3

$\frac{1}{2} x + \frac{1}{3} y = 3$

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 left side.

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{1}{3} y = 3$

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

$\frac{x}{2} + \frac{y}{3} = 3$

Subtract $\frac{x}{2}$ from both sides of the equation.

$\frac{y}{3} = 3 - \frac{x}{2}$

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (3 - \frac{x}{2})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{y}{3} = 3 (3 - \frac{x}{2})$

Rewrite the expression.

$y = 3 (3 - \frac{x}{2})$

Simplify the right side.

Simplify $3 (3 - \frac{x}{2})$ .

Apply the distributive property.

$y = 3 \cdot 3 + 3 (- \frac{x}{2})$

Multiply $3$ by $3$ .

$y = 9 + 3 (- \frac{x}{2})$

Multiply $3 (- \frac{x}{2})$ .

Multiply $- 1$ by $3$ .

$y = 9 - 3 \frac{x}{2}$

Combine $- 3$ and $\frac{x}{2}$ .

$y = 9 + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = 9 - \frac{3 x}{2}$

Reorder $9$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + 9$

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

Reorder terms.

$y = - (\frac{3}{2} x) + 9$

Remove parentheses.

$y = - \frac{3}{2} x + 9$