Finite Math Examples

$\frac{2}{7} x + \frac{5}{9} y = 16$

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 $\frac{2}{7}$ and $x$ .

$\frac{2 x}{7} + \frac{5}{9} y = 16$

Step 2.1.1.2

Combine $\frac{5}{9}$ and $y$ .

$\frac{2 x}{7} + \frac{5 y}{9} = 16$

Step 2.2

Subtract $\frac{2 x}{7}$ from both sides of the equation.

$\frac{5 y}{9} = 16 - \frac{2 x}{7}$

Step 2.3

Multiply both sides of the equation by $\frac{9}{5}$ .

$\frac{9}{5} \cdot \frac{5 y}{9} = \frac{9}{5} (16 - \frac{2 x}{7})$

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

Simplify $\frac{9}{5} \cdot \frac{5 y}{9}$ .

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Step 2.4.1.1.1

Cancel the common factor of $9$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 y}{9} = \frac{9}{5} (16 - \frac{2 x}{7})$

Step 2.4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{9}{5} (16 - \frac{2 x}{7})$

Step 2.4.1.1.2

Cancel the common factor of $5$ .

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Step 2.4.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{9}{5} (16 - \frac{2 x}{7})$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{9}{5} (16 - \frac{2 x}{7})$

Step 2.4.1.1.2.3

Rewrite the expression.

$y = \frac{9}{5} (16 - \frac{2 x}{7})$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $\frac{9}{5} (16 - \frac{2 x}{7})$ .

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Step 2.4.2.1.1

Apply the distributive property.

$y = \frac{9}{5} \cdot 16 + \frac{9}{5} (- \frac{2 x}{7})$

Step 2.4.2.1.2

Multiply $\frac{9}{5} \cdot 16$ .

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Step 2.4.2.1.2.1

Combine $\frac{9}{5}$ and $16$ .

$y = \frac{9 \cdot 16}{5} + \frac{9}{5} (- \frac{2 x}{7})$

Step 2.4.2.1.2.2

Multiply $9$ by $16$ .

$y = \frac{144}{5} + \frac{9}{5} (- \frac{2 x}{7})$

Step 2.4.2.1.3

Multiply $\frac{9}{5} (- \frac{2 x}{7})$ .

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Step 2.4.2.1.3.1

Multiply $\frac{9}{5}$ by $\frac{2 x}{7}$ .

$y = \frac{144}{5} - \frac{9 (2 x)}{5 \cdot 7}$

Step 2.4.2.1.3.2

Multiply $2$ by $9$ .

$y = \frac{144}{5} - \frac{18 x}{5 \cdot 7}$

Step 2.4.2.1.3.3

Multiply $5$ by $7$ .

$y = \frac{144}{5} - \frac{18 x}{35}$

Step 2.5

Reorder $\frac{144}{5}$ and $- \frac{18 x}{35}$ .

$y = - \frac{18 x}{35} + \frac{144}{5}$

Step 2.6

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

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Step 2.6.1

Reorder terms.

$y = - (\frac{18}{35} x) + \frac{144}{5}$

Step 2.6.2

Remove parentheses.

$y = - \frac{18}{35} x + \frac{144}{5}$