Algebra Examples

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

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 right side.

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Step 2.1.1

Simplify $- \frac{1}{3} (2 x + 6)$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

Multiply $2$ by $- 1$ .

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

Step 2.1.1.2.2

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

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

Step 2.1.1.2.3

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

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

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Step 2.1.1.3.2

Factor $3$ out of $6$ .

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

Step 2.1.1.3.3

Cancel the common factor.

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

Step 2.1.1.3.4

Rewrite the expression.

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

Step 2.1.1.4

Simplify the expression.

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Step 2.1.1.4.1

Multiply $- 1$ by $2$ .

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

Step 2.1.1.4.2

Move the negative in front of the fraction.

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

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.

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

Step 2.2.2

Subtract $3$ from $- 2$ .

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

Step 2.3

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

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Step 2.3.1

Reorder terms.

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

Step 2.3.2

Remove parentheses.

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