Pre-Algebra Examples

$\frac{4}{9} x - \frac{4}{3} y = 2$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $\frac{4 x}{9}$ from both sides of the equation.

$- \frac{4 y}{3} = 2 - \frac{4 x}{9}$

Step 1.2

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 y}{3}) = - \frac{3}{4} (2 - \frac{4 x}{9})$

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 $- \frac{3}{4} (- \frac{4 y}{3})$ .

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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 $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 y}{3}) = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.1.2

Move the leading negative in $- \frac{4 y}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 y}{3} = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 y}{3} = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 y}{3} = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 y) = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.2

Cancel the common factor of $4$ .

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Step 1.3.1.1.2.1

Factor $4$ out of $- 4 y$ .

$\frac{- 1}{4} (4 (- y)) = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- y)) = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.2.3

Rewrite the expression.

$- - y = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.3

Multiply.

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Step 1.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{4} (2 - \frac{4 x}{9})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $- \frac{3}{4} (2 - \frac{4 x}{9})$ .

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Step 1.3.2.1.1

Simplify terms.

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Step 1.3.2.1.1.1

Apply the distributive property.

$y = - \frac{3}{4} \cdot 2 - \frac{3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.2

Cancel the common factor of $2$ .

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Step 1.3.2.1.1.2.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$y = \frac{- 3}{4} \cdot 2 - \frac{3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.2.2

Factor $2$ out of $4$ .

$y = \frac{- 3}{2 (2)} \cdot 2 - \frac{3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.2.3

Cancel the common factor.

$y = \frac{- 3}{2 \cdot 2} \cdot 2 - \frac{3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.2.4

Rewrite the expression.

$y = \frac{- 3}{2} - \frac{3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.3

Cancel the common factor of $3$ .

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Step 1.3.2.1.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$y = \frac{- 3}{2} + \frac{- 3}{4} (- \frac{4 x}{9})$

Step 1.3.2.1.1.3.2

Move the leading negative in $- \frac{4 x}{9}$ into the numerator.

$y = \frac{- 3}{2} + \frac{- 3}{4} \cdot \frac{- 4 x}{9}$

Step 1.3.2.1.1.3.3

Factor $3$ out of $- 3$ .

$y = \frac{- 3}{2} + \frac{3 (- 1)}{4} \cdot \frac{- 4 x}{9}$

Step 1.3.2.1.1.3.4

Factor $3$ out of $9$ .

$y = \frac{- 3}{2} + \frac{3 \cdot - 1}{4} \cdot \frac{- 4 x}{3 \cdot 3}$

Step 1.3.2.1.1.3.5

Cancel the common factor.

$y = \frac{- 3}{2} + \frac{3 \cdot - 1}{4} \cdot \frac{- 4 x}{3 \cdot 3}$

Step 1.3.2.1.1.3.6

Rewrite the expression.

$y = \frac{- 3}{2} + \frac{- 1}{4} \cdot \frac{- 4 x}{3}$

Step 1.3.2.1.1.4

Cancel the common factor of $4$ .

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Step 1.3.2.1.1.4.1

Factor $4$ out of $- 4 x$ .

$y = \frac{- 3}{2} + \frac{- 1}{4} \cdot \frac{4 (- x)}{3}$

Step 1.3.2.1.1.4.2

Cancel the common factor.

$y = \frac{- 3}{2} + \frac{- 1}{4} \cdot \frac{4 (- x)}{3}$

Step 1.3.2.1.1.4.3

Rewrite the expression.

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

Step 1.3.2.1.2

Simplify each term.

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Step 1.3.2.1.2.1

Move the negative in front of the fraction.

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

Step 1.3.2.1.2.2

Move the negative in front of the fraction.

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

Step 1.3.2.1.2.3

Multiply $- - \frac{x}{3}$ .

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Step 1.3.2.1.2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.3.2.1.2.3.2

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

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

Step 1.4

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

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

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.

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

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 $y = m x + b$ .

$m = \frac{1}{3}$

$b = - \frac{3}{2}$

Step 3.2

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

Slope: $\frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

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.

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

Step 4.2

Find the x-intercept.

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Step 4.2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{1}{3} x - \frac{3}{2}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{1}{3} x - \frac{3}{2} = 0$ .

$\frac{1}{3} x - \frac{3}{2} = 0$

Step 4.2.2.2

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

$\frac{x}{3} - \frac{3}{2} = 0$

Step 4.2.2.3

Add $\frac{3}{2}$ to both sides of the equation.

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

Step 4.2.2.4

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (\frac{3}{2})$

Step 4.2.2.5

Simplify both sides of the equation.

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Step 4.2.2.5.1

Simplify the left side.

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Step 4.2.2.5.1.1

Cancel the common factor of $3$ .

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Step 4.2.2.5.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 (\frac{3}{2})$

Step 4.2.2.5.1.1.2

Rewrite the expression.

$x = 3 (\frac{3}{2})$

Step 4.2.2.5.2

Simplify the right side.

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Step 4.2.2.5.2.1

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

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Step 4.2.2.5.2.1.1

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

$x = \frac{3 \cdot 3}{2}$

Step 4.2.2.5.2.1.2

Multiply $3$ by $3$ .

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

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{9}{2}, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{1}{3} \cdot (0) - \frac{3}{2}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply $\frac{1}{3}$ by $0$ .

$y = \frac{1}{3} \cdot 0 - \frac{3}{2}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{1}{3} \cdot (0) - \frac{3}{2}$

Step 4.3.2.3

Simplify $\frac{1}{3} \cdot (0) - \frac{3}{2}$ .

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Step 4.3.2.3.1

Multiply $\frac{1}{3}$ by $0$ .

$y = 0 - \frac{3}{2}$

Step 4.3.2.3.2

Subtract $\frac{3}{2}$ from $0$ .

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

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Step 4.4

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

$\begin{array}{c} x & y \\ 0 & - \frac{3}{2} \\ \frac{9}{2} & 0 \end{array}$

Step 5

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

Slope: $\frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

$\begin{array}{c} x & y \\ 0 & - \frac{3}{2} \\ \frac{9}{2} & 0 \end{array}$

Step 6