Write in Slope-Intercept Form 2y+3=-1/3(x-2)

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

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

$y = m x + b$

Rewrite in slope-intercept form.

Simplify the right side.

Simplify $- \frac{1}{3} (x - 2)$ .

Apply the distributive property.

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

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

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

Multiply $- \frac{1}{3} \cdot - 2$ .

Multiply $- 2$ by $- 1$ .

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

Combine $2$ and $\frac{1}{3}$ .

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

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

Subtract $3$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $3$ .

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

Subtract $9$ from $2$ .

$2 y = - \frac{x}{3} + \frac{- 7}{3}$

Move the negative in front of the fraction.

$2 y = - \frac{x}{3} - \frac{7}{3}$

Divide each term in $2 y = - \frac{x}{3} - \frac{7}{3}$ by $2$ and simplify.

Divide each term in $2 y = - \frac{x}{3} - \frac{7}{3}$ by $2$ .

$\frac{2 y}{2} = \frac{- \frac{x}{3}}{2} + \frac{- \frac{7}{3}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- \frac{x}{3}}{2} + \frac{- \frac{7}{3}}{2}$

Divide $y$ by $1$ .

$y = \frac{- \frac{x}{3}}{2} + \frac{- \frac{7}{3}}{2}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{x}{3} \cdot \frac{1}{2} + \frac{- \frac{7}{3}}{2}$

Multiply $- \frac{x}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{x}{3}$ .

$y = - \frac{x}{2 \cdot 3} + \frac{- \frac{7}{3}}{2}$

Multiply $2$ by $3$ .

$y = - \frac{x}{6} + \frac{- \frac{7}{3}}{2}$

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{x}{6} - \frac{7}{3} \cdot \frac{1}{2}$

Multiply $- \frac{7}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{7}{3}$ .

$y = - \frac{x}{6} - \frac{7}{2 \cdot 3}$

Multiply $2$ by $3$ .

$y = - \frac{x}{6} - \frac{7}{6}$

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

Reorder terms.

$y = - (\frac{1}{6} x) - \frac{7}{6}$

Remove parentheses.

$y = - \frac{1}{6} x - \frac{7}{6}$

Write in Slope-Intercept Form 2y+3=-1/3(x-2)

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