Pre-Algebra Examples

$\frac{1}{3} \cdot (y + 3) - \frac{1}{9} \cdot (y - 1) = - 2$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{1}{3} \cdot (y + 3) - \frac{1}{9} \cdot (y - 1)$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$\frac{1}{3} y + \frac{1}{3} \cdot 3 - \frac{1}{9} \cdot (y - 1) = - 2$

Step 1.2.1.1.2

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

$\frac{y}{3} + \frac{1}{3} \cdot 3 - \frac{1}{9} \cdot (y - 1) = - 2$

Step 1.2.1.1.3

Cancel the common factor of $3$ .

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Step 1.2.1.1.3.1

Cancel the common factor.

$\frac{y}{3} + \frac{1}{3} \cdot 3 - \frac{1}{9} \cdot (y - 1) = - 2$

Step 1.2.1.1.3.2

Rewrite the expression.

$\frac{y}{3} + 1 - \frac{1}{9} \cdot (y - 1) = - 2$

Step 1.2.1.1.4

Apply the distributive property.

$\frac{y}{3} + 1 - \frac{1}{9} y - \frac{1}{9} \cdot - 1 = - 2$

Step 1.2.1.1.5

Combine $y$ and $\frac{1}{9}$ .

$\frac{y}{3} + 1 - \frac{y}{9} - \frac{1}{9} \cdot - 1 = - 2$

Step 1.2.1.1.6

Multiply $- \frac{1}{9} \cdot - 1$ .

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Step 1.2.1.1.6.1

Multiply $- 1$ by $- 1$ .

$\frac{y}{3} + 1 - \frac{y}{9} + 1 (\frac{1}{9}) = - 2$

Step 1.2.1.1.6.2

Multiply $\frac{1}{9}$ by $1$ .

$\frac{y}{3} + 1 - \frac{y}{9} + \frac{1}{9} = - 2$

Step 1.2.1.2

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

$\frac{y}{3} \cdot \frac{3}{3} - \frac{y}{9} + 1 + \frac{1}{9} = - 2$

Step 1.2.1.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1.3.1

Multiply $\frac{y}{3}$ by $\frac{3}{3}$ .

$\frac{y \cdot 3}{3 \cdot 3} - \frac{y}{9} + 1 + \frac{1}{9} = - 2$

Step 1.2.1.3.2

Multiply $3$ by $3$ .

$\frac{y \cdot 3}{9} - \frac{y}{9} + 1 + \frac{1}{9} = - 2$

Step 1.2.1.4

Simplify terms.

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Step 1.2.1.4.1

Combine the numerators over the common denominator.

$\frac{y \cdot 3 - y}{9} + 1 + \frac{1}{9} = - 2$

Step 1.2.1.4.2

Combine the numerators over the common denominator.

$1 + \frac{y \cdot 3 - y + 1}{9} = - 2$

Step 1.2.1.4.3

Move $3$ to the left of $y$ .

$1 + \frac{3 y - y + 1}{9} = - 2$

Step 1.2.1.4.4

Simplify terms.

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Step 1.2.1.4.4.1

Subtract $y$ from $3 y$ .

$1 + \frac{2 y + 1}{9} = - 2$

Step 1.2.1.4.4.2

Write $1$ as a fraction with a common denominator.

$\frac{9}{9} + \frac{2 y + 1}{9} = - 2$

Step 1.2.1.4.4.3

Combine the numerators over the common denominator.

$\frac{9 + 2 y + 1}{9} = - 2$

Step 1.2.1.5

Simplify the numerator.

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Step 1.2.1.5.1

Add $9$ and $1$ .

$\frac{2 y + 10}{9} = - 2$

Step 1.2.1.5.2

Factor $2$ out of $2 y + 10$ .

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Step 1.2.1.5.2.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) + 10}{9} = - 2$

Step 1.2.1.5.2.2

Factor $2$ out of $10$ .

$\frac{2 y + 2 \cdot 5}{9} = - 2$

Step 1.2.1.5.2.3

Factor $2$ out of $2 y + 2 \cdot 5$ .

$\frac{2 (y + 5)}{9} = - 2$

Step 1.3

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 (y + 5)}{9} = \frac{9}{2} \cdot - 2$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $\frac{9}{2} \cdot \frac{2 (y + 5)}{9}$ .

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Step 1.4.1.1.1

Cancel the common factor of $9$ .

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Step 1.4.1.1.1.1

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 (y + 5)}{9} = \frac{9}{2} \cdot - 2$

Step 1.4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 (y + 5)) = \frac{9}{2} \cdot - 2$

Step 1.4.1.1.2

Cancel the common factor of $2$ .

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Step 1.4.1.1.2.1

Cancel the common factor.

$\frac{1}{2} (2 (y + 5)) = \frac{9}{2} \cdot - 2$

Step 1.4.1.1.2.2

Rewrite the expression.

$y + 5 = \frac{9}{2} \cdot - 2$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $\frac{9}{2} \cdot - 2$ .

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Step 1.4.2.1.1

Cancel the common factor of $2$ .

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Step 1.4.2.1.1.1

Factor $2$ out of $- 2$ .

$y + 5 = \frac{9}{2} \cdot (2 (- 1))$

Step 1.4.2.1.1.2

Cancel the common factor.

$y + 5 = \frac{9}{2} \cdot (2 \cdot - 1)$

Step 1.4.2.1.1.3

Rewrite the expression.

$y + 5 = 9 \cdot - 1$

Step 1.4.2.1.2

Multiply $9$ by $- 1$ .

$y + 5 = - 9$

Step 1.5

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

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Step 1.5.1

Subtract $5$ from both sides of the equation.

$y = - 9 - 5$

Step 1.5.2

Subtract $5$ from $- 9$ .

$y = - 14$

Step 2

Using the slope-intercept form, the y-intercept is $- 14$ .

$b = - 14$

Step 3

y-intercept in point form.

$(0, - 14)$

Step 4