Pre-Algebra Examples

$\frac{3}{2} x - \frac{1}{3} y = 5$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

Step 1.2

Multiply both sides of the equation by $- 3$ .

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

Step 1.3

Simplify both sides of the equation.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 1.3.1.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1.1

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

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

Step 1.3.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 (5 - \frac{3 x}{2})$

Step 1.3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- y}{3} = - 3 (5 - \frac{3 x}{2})$

Step 1.3.1.1.1.4

Rewrite the expression.

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

Step 1.3.1.1.2

Multiply.

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Step 1.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 (5 - \frac{3 x}{2})$

Step 1.3.1.1.2.2

Multiply $y$ by $1$ .

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

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- 3 (5 - \frac{3 x}{2})$ .

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Step 1.3.2.1.1

Apply the distributive property.

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

Step 1.3.2.1.2

Multiply $- 3$ by $5$ .

$y = - 15 - 3 (- \frac{3 x}{2})$

Step 1.3.2.1.3

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

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Step 1.3.2.1.3.1

Multiply $- 1$ by $- 3$ .

$y = - 15 + 3 \frac{3 x}{2}$

Step 1.3.2.1.3.2

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

$y = - 15 + \frac{3 (3 x)}{2}$

Step 1.3.2.1.3.3

Multiply $3$ by $3$ .

$y = - 15 + \frac{9 x}{2}$

Step 1.4

Reorder $- 15$ and $\frac{9 x}{2}$ .

$y = \frac{9 x}{2} - 15$

Step 2

Rewrite in slope-intercept form.

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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

Reorder terms.

$y = \frac{9}{2} x - 15$

Step 3

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

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Step 3.1

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

$m = \frac{9}{2}$

$b = - 15$

Step 3.2

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

Slope: $\frac{9}{2}$

y-intercept: $(0, - 15)$

Slope: $\frac{9}{2}$

y-intercept: $(0, - 15)$

Step 4

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 4.1

Reorder terms.

$y = \frac{9}{2} x - 15$

Step 4.2

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 15 \\ 2 & - 6 \end{array}$

Step 5

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

Slope: $\frac{9}{2}$

y-intercept: $(0, - 15)$

$\begin{array}{c} x & y \\ 0 & - 15 \\ 2 & - 6 \end{array}$

Step 6