Algebra Examples

$\frac{1}{3} x + 2 y = \frac{4}{3}$

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

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

$\frac{x}{3} + 2 y = \frac{4}{3}$

Step 2.2

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

$2 y = \frac{4}{3} - \frac{x}{3}$

Step 2.3

Divide each term in $2 y = \frac{4}{3} - \frac{x}{3}$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 y = \frac{4}{3} - \frac{x}{3}$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{4}{3}}{2} + \frac{- \frac{x}{3}}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{4}{3} \cdot \frac{1}{2} + \frac{- \frac{x}{3}}{2}$

Step 2.3.3.1.2

Cancel the common factor of $2$ .

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Step 2.3.3.1.2.1

Factor $2$ out of $4$ .

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

Step 2.3.3.1.2.2

Cancel the common factor.

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

Step 2.3.3.1.2.3

Rewrite the expression.

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

Step 2.3.3.1.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.1.4

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

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Step 2.3.3.1.4.1

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

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

Step 2.3.3.1.4.2

Multiply $2$ by $3$ .

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

Step 2.4

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

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Step 2.4.1

Reorder $\frac{2}{3}$ and $- \frac{x}{6}$ .

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

Step 2.4.2

Reorder terms.

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

Step 2.4.3

Remove parentheses.

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