Write in y=mx+b Form (3x-3y)/3=(5x-2)/6

$\frac{3 x - 3 y}{3} = \frac{5 x - 2}{6}$

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.

Cancel the common factor of $3 x - 3 y$ and $3$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 3 y}{3} = \frac{5 x - 2}{6}$

Factor $3$ out of $- 3 y$ .

$\frac{3 (x) + 3 (- y)}{3} = \frac{5 x - 2}{6}$

Factor $3$ out of $3 (x) + 3 (- y)$ .

$\frac{3 (x - y)}{3} = \frac{5 x - 2}{6}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (x - y)}{3 (1)} = \frac{5 x - 2}{6}$

Cancel the common factor.

$\frac{3 (x - y)}{3 \cdot 1} = \frac{5 x - 2}{6}$

Rewrite the expression.

$\frac{x - y}{1} = \frac{5 x - 2}{6}$

Divide $x - y$ by $1$ .

$x - y = \frac{5 x - 2}{6}$

Simplify $\frac{5 x - 2}{6}$ .

Split the fraction $\frac{5 x - 2}{6}$ into two fractions.

$x - y = \frac{5 x}{6} + \frac{- 2}{6}$

Simplify each term.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$x - y = \frac{5 x}{6} + \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x - y = \frac{5 x}{6} + \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$x - y = \frac{5 x}{6} + \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$x - y = \frac{5 x}{6} + \frac{- 1}{3}$

Move the negative in front of the fraction.

$x - y = \frac{5 x}{6} - \frac{1}{3}$

Subtract $x$ from both sides of the equation.

$- y = \frac{5 x}{6} - \frac{1}{3} - x$

Divide each term in $- y = \frac{5 x}{6} - \frac{1}{3} - x$ by $- 1$ and simplify.

Divide each term in $- y = \frac{5 x}{6} - \frac{1}{3} - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{\frac{5 x}{6}}{- 1} + \frac{- \frac{1}{3}}{- 1} + \frac{- x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{\frac{5 x}{6}}{- 1} + \frac{- \frac{1}{3}}{- 1} + \frac{- x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{\frac{5 x}{6}}{- 1} + \frac{- \frac{1}{3}}{- 1} + \frac{- x}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{5 x}{6}}{- 1}$ .

$y = - 1 \cdot \frac{5 x}{6} + \frac{- \frac{1}{3}}{- 1} + \frac{- x}{- 1}$

Rewrite $- 1 \cdot \frac{5 x}{6}$ as $- \frac{5 x}{6}$ .

$y = - \frac{5 x}{6} + \frac{- \frac{1}{3}}{- 1} + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$y = - \frac{5 x}{6} + \frac{\frac{1}{3}}{1} + \frac{- x}{- 1}$

Divide $\frac{1}{3}$ by $1$ .

$y = - \frac{5 x}{6} + \frac{1}{3} + \frac{- x}{- 1}$

Dividing two negative values results in a positive value.

$y = - \frac{5 x}{6} + \frac{1}{3} + \frac{x}{1}$

Divide $x$ by $1$ .

$y = - \frac{5 x}{6} + \frac{1}{3} + x$

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

Simplify $- \frac{5 x}{6} + \frac{1}{3} + x$ .

To write $x$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = - \frac{5 x}{6} + x \cdot \frac{6}{6} + \frac{1}{3}$

Combine $x$ and $\frac{6}{6}$ .

$y = - \frac{5 x}{6} + \frac{x \cdot 6}{6} + \frac{1}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 5 x + x \cdot 6}{6} + \frac{1}{3}$

Add $- 5 x$ and $x \cdot 6$ .

Reorder $x$ and $6$ .

$y = \frac{- 5 x + 6 \cdot x}{6} + \frac{1}{3}$

Add $- 5 x$ and $6 \cdot x$ .

$y = \frac{x}{6} + \frac{1}{3}$

Reorder terms.

$y = \frac{1}{6} x + \frac{1}{3}$

Write in y=mx+b Form (3x-3y)/3=(5x-2)/6

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