Algebra Examples

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

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 right side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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Step 2.1.1.3.1

Multiply $- 2$ by $- 1$ .

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

Step 2.1.1.3.2

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

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

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $- 3$ by $3$ .

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

Step 2.2.5.2

Subtract $9$ from $2$ .

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

Step 2.2.6

Move the negative in front of the fraction.

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

Step 2.3

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

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Step 2.3.1

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

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

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.

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

Step 2.3.2.1.2

Divide $y$ by $1$ .

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

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.

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

Step 2.3.3.1.2

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

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Step 2.3.3.1.2.1

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

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

Step 2.3.3.1.2.2

Multiply $2$ by $3$ .

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

Step 2.3.3.1.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.1.4

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

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Step 2.3.3.1.4.1

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

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

Step 2.3.3.1.4.2

Multiply $2$ by $3$ .

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

Step 2.4

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

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Step 2.4.1

Reorder terms.

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

Step 2.4.2

Remove parentheses.

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