Finite Math Examples

$\frac{x}{2} + \frac{5 y}{4} = 6$

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

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

$\frac{5 y}{4} = 6 - \frac{x}{2}$

Step 2.2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Simplify $\frac{4}{5} \cdot \frac{5 y}{4}$ .

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Step 2.3.1.1.1

Cancel the common factor of $4$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 y}{4} = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3.1.1.2

Cancel the common factor of $5$ .

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Step 2.3.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3.1.1.2.3

Rewrite the expression.

$y = \frac{4}{5} (6 - \frac{x}{2})$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\frac{4}{5} (6 - \frac{x}{2})$ .

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Step 2.3.2.1.1

Apply the distributive property.

$y = \frac{4}{5} \cdot 6 + \frac{4}{5} (- \frac{x}{2})$

Step 2.3.2.1.2

Multiply $\frac{4}{5} \cdot 6$ .

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Step 2.3.2.1.2.1

Combine $\frac{4}{5}$ and $6$ .

$y = \frac{4 \cdot 6}{5} + \frac{4}{5} (- \frac{x}{2})$

Step 2.3.2.1.2.2

Multiply $4$ by $6$ .

$y = \frac{24}{5} + \frac{4}{5} (- \frac{x}{2})$

Step 2.3.2.1.3

Cancel the common factor of $2$ .

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Step 2.3.2.1.3.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$y = \frac{24}{5} + \frac{4}{5} \cdot \frac{- x}{2}$

Step 2.3.2.1.3.2

Factor $2$ out of $4$ .

$y = \frac{24}{5} + \frac{2 (2)}{5} \cdot \frac{- x}{2}$

Step 2.3.2.1.3.3

Cancel the common factor.

$y = \frac{24}{5} + \frac{2 \cdot 2}{5} \cdot \frac{- x}{2}$

Step 2.3.2.1.3.4

Rewrite the expression.

$y = \frac{24}{5} + \frac{2}{5} (- x)$

Step 2.3.2.1.4

Combine $\frac{2}{5}$ and $x$ .

$y = \frac{24}{5} - \frac{2 x}{5}$

Step 2.4

Reorder $\frac{24}{5}$ and $- \frac{2 x}{5}$ .

$y = - \frac{2 x}{5} + \frac{24}{5}$

Step 2.5

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

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Step 2.5.1

Reorder terms.

$y = - (\frac{2}{5} x) + \frac{24}{5}$

Step 2.5.2

Remove parentheses.

$y = - \frac{2}{5} x + \frac{24}{5}$