Pre-Algebra Examples

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

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Add $\frac{1}{2}$ to both sides of the equation.

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

Step 1.1.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.4.1

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

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

Step 1.1.4.2

Multiply $3$ by $2$ .

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

Step 1.1.4.3

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

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

Step 1.1.4.4

Multiply $2$ by $3$ .

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

Step 1.1.5

Combine the numerators over the common denominator.

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

Step 1.1.6

Add $- 2$ and $3$ .

$2 y = \frac{1}{6}$

Step 1.2

Divide each term in $2 y = \frac{1}{6}$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = \frac{1}{6}$ by $2$ .

$\frac{2 y}{2} = \frac{\frac{1}{6}}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{\frac{1}{6}}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{1}{6}}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{1}{6} \cdot \frac{1}{2}$

Step 1.2.3.2

Multiply $\frac{1}{6} \cdot \frac{1}{2}$ .

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Step 1.2.3.2.1

Multiply $\frac{1}{6}$ by $\frac{1}{2}$ .

$y = \frac{1}{6 \cdot 2}$

Step 1.2.3.2.2

Multiply $6$ by $2$ .

$y = \frac{1}{12}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

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 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 0$

$b = \frac{1}{12}$

Step 2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $0$

y-intercept: $(0, \frac{1}{12})$

Slope: $0$

y-intercept: $(0, \frac{1}{12})$

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & \frac{1}{12} \\ 1 & \frac{1}{12} \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: $0$

y-intercept: $(0, \frac{1}{12})$

$\begin{array}{c} x & y \\ 0 & \frac{1}{12} \\ 1 & \frac{1}{12} \end{array}$

Step 5