Pre-Algebra Examples

$\frac{3}{4} x + \frac{1}{2} y = 12$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $\frac{3 x}{4}$ from both sides of the equation.

$\frac{y}{2} = 12 - \frac{3 x}{4}$

Step 1.2

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (12 - \frac{3 x}{4})$

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

Cancel the common factor of $2$ .

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Step 1.3.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (12 - \frac{3 x}{4})$

Step 1.3.1.1.2

Rewrite the expression.

$y = 2 (12 - \frac{3 x}{4})$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $2 (12 - \frac{3 x}{4})$ .

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Step 1.3.2.1.1

Apply the distributive property.

$y = 2 \cdot 12 + 2 (- \frac{3 x}{4})$

Step 1.3.2.1.2

Multiply $2$ by $12$ .

$y = 24 + 2 (- \frac{3 x}{4})$

Step 1.3.2.1.3

Cancel the common factor of $2$ .

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Step 1.3.2.1.3.1

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

$y = 24 + 2 \frac{- 3 x}{4}$

Step 1.3.2.1.3.2

Factor $2$ out of $4$ .

$y = 24 + 2 \frac{- 3 x}{2 (2)}$

Step 1.3.2.1.3.3

Cancel the common factor.

$y = 24 + 2 \frac{- 3 x}{2 \cdot 2}$

Step 1.3.2.1.3.4

Rewrite the expression.

$y = 24 + \frac{- 3 x}{2}$

Step 1.3.2.1.4

Move the negative in front of the fraction.

$y = 24 - \frac{3 x}{2}$

Step 1.4

Reorder $24$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + 24$

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

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

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Step 2.2.1

Reorder terms.

$y = - (\frac{3}{2} x) + 24$

Step 2.2.2

Remove parentheses.

$y = - \frac{3}{2} x + 24$

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 $y = m x + b$ .

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

$b = 24$

Step 3.2

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, 24)$

Slope: $- \frac{3}{2}$

y-intercept: $(0, 24)$

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

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

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Step 4.1.1

Reorder terms.

$y = - (\frac{3}{2} x) + 24$

Step 4.1.2

Remove parentheses.

$y = - \frac{3}{2} x + 24$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 24 \\ 2 & 21 \end{array}$

Step 5

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

Slope: $- \frac{3}{2}$

y-intercept: $(0, 24)$

$\begin{array}{c} x & y \\ 0 & 24 \\ 2 & 21 \end{array}$

Step 6