Write in y=mx+b Form 2/3x-1/2y=6

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

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

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

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

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

Subtract $\frac{2 x}{3}$ from both sides of the equation.

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

Multiply both sides of the equation by $- 2$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{y}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{y}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- y}{2} = - 2 (6 - \frac{2 x}{3})$

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 2 (6 - \frac{2 x}{3})$

Multiply $y$ by $1$ .

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

Simplify the right side.

Simplify $- 2 (6 - \frac{2 x}{3})$ .

Apply the distributive property.

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

Multiply $- 2$ by $6$ .

$y = - 12 - 2 (- \frac{2 x}{3})$

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

Multiply $- 1$ by $- 2$ .

$y = - 12 + 2 \frac{2 x}{3}$

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

$y = - 12 + \frac{2 (2 x)}{3}$

Multiply $2$ by $2$ .

$y = - 12 + \frac{4 x}{3}$

Reorder $- 12$ and $\frac{4 x}{3}$ .

$y = \frac{4 x}{3} - 12$

Reorder terms.

$y = \frac{4}{3} x - 12$

Write in y=mx+b Form 2/3x-1/2y=6

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