Pre-Algebra Examples

$\frac{3}{4} x + \frac{1}{2} y = \frac{1}{8}$

Step 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

Rewrite in slope-intercept form.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + \frac{1}{2} y = \frac{1}{8}$

Step 2.1.1.2

Combine $\frac{1}{2}$ and $y$ .

$\frac{3 x}{4} + \frac{y}{2} = \frac{1}{8}$

$\frac{3 x}{4} + \frac{y}{2} = \frac{1}{8}$

$\frac{3 x}{4} + \frac{y}{2} = \frac{1}{8}$

Step 2.2

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

$\frac{y}{2} = \frac{1}{8} - \frac{3 x}{4}$

Step 2.3

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (\frac{1}{8} - \frac{3 x}{4})$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Cancel the common factor of $2$ .

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Step 2.4.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (\frac{1}{8} - \frac{3 x}{4})$

Step 2.4.1.1.2

Rewrite the expression.

$y = 2 (\frac{1}{8} - \frac{3 x}{4})$

$y = 2 (\frac{1}{8} - \frac{3 x}{4})$

$y = 2 (\frac{1}{8} - \frac{3 x}{4})$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $2 (\frac{1}{8} - \frac{3 x}{4})$ .

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Step 2.4.2.1.1

Apply the distributive property.

$y = 2 (\frac{1}{8}) + 2 (- \frac{3 x}{4})$

Step 2.4.2.1.2

Cancel the common factor of $2$ .

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Step 2.4.2.1.2.1

Factor $2$ out of $8$ .

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

Step 2.4.2.1.2.2

Cancel the common factor.

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

Step 2.4.2.1.2.3

Rewrite the expression.

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

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

Step 2.4.2.1.3

Cancel the common factor of $2$ .

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Step 2.4.2.1.3.1

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

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

Step 2.4.2.1.3.2

Factor $2$ out of $4$ .

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

Step 2.4.2.1.3.3

Cancel the common factor.

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

Step 2.4.2.1.3.4

Rewrite the expression.

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

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

Step 2.4.2.1.4

Move the negative in front of the fraction.

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

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

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

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

Step 2.5

Reorder $\frac{1}{4}$ and $- \frac{3 x}{2}$ .

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

Step 2.6

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

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Step 2.6.1

Reorder terms.

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

Step 2.6.2

Remove parentheses.

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$