Write in Slope-Intercept Form 2x+3y-6=0

$2 x + 3 y - 6 = 0$

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 $2 x$ from both sides of the equation.

$3 y - 6 = - 2 x$

Add $6$ to both sides of the equation.

$3 y = - 2 x + 6$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Divide $6$ by $3$ .

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

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

Reorder terms.

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

Remove parentheses.

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