Write in y=mx+b Form 3x-2y+6=0

$3 x - 2 y + 6 = 0$

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.

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

Subtract $3 x$ from both sides of the equation.

$- 2 y + 6 = - 3 x$

Subtract $6$ from both sides of the equation.

$- 2 y = - 3 x - 6$

Divide each term in $- 2 y = - 3 x - 6$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 3 x - 6$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 3 x}{- 2} + \frac{- 6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 3 x}{- 2} + \frac{- 6}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{- 2} + \frac{- 6}{- 2}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{(3) x}{2} + \frac{- 6}{- 2}$

Divide $- 6$ by $- 2$ .

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

Reorder terms.

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