Algebra Examples

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

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.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Factor $3$ out of $3 x$ .

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Cancel the common factors.

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Step 2.1.1.4.1

Factor $3$ out of $3$ .

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

Step 2.1.1.4.2

Cancel the common factor.

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

Step 2.1.1.4.3

Rewrite the expression.

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

Step 2.1.1.4.4

Divide $x - y$ by $1$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

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

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Step 2.2.2.1.1

Factor $2$ out of $- 2$ .

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

Step 2.2.2.1.2

Cancel the common factors.

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Step 2.2.2.1.2.1

Factor $2$ out of $6$ .

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

Step 2.2.2.1.2.2

Cancel the common factor.

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

Step 2.2.2.1.2.3

Rewrite the expression.

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

Step 2.2.2.2

Move the negative in front of the fraction.

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

Step 2.3

Subtract $x$ from both sides of the equation.

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

Step 2.4

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

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Step 2.4.1

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

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

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Dividing two negative values results in a positive value.

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

Step 2.4.2.2

Divide $y$ by $1$ .

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

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

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

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

Step 2.4.3.1.2

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

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

Step 2.4.3.1.3

Dividing two negative values results in a positive value.

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

Step 2.4.3.1.4

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

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

Step 2.4.3.1.5

Dividing two negative values results in a positive value.

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

Step 2.4.3.1.6

Divide $x$ by $1$ .

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

Step 2.5

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

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Step 2.5.1

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

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Step 2.5.1.1

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

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

Step 2.5.1.2

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

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

Step 2.5.1.3

Combine the numerators over the common denominator.

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

Step 2.5.1.4

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

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Step 2.5.1.4.1

Reorder $x$ and $6$ .

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

Step 2.5.1.4.2

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

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

Step 2.5.2

Reorder terms.

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