Algebra Examples

$- \frac{x}{5} + \frac{2 y}{3} = - 6 \frac{1}{6}$

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

Simplify the right side.

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Step 2.1.1

Convert $6 \frac{1}{6}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{x}{5} + \frac{2 y}{3} = - (6 + \frac{1}{6})$

Step 2.1.1.2

Add $6$ and $\frac{1}{6}$ .

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Step 2.1.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{x}{5} + \frac{2 y}{3} = - (6 \cdot \frac{6}{6} + \frac{1}{6})$

Step 2.1.1.2.2

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

$- \frac{x}{5} + \frac{2 y}{3} = - (\frac{6 \cdot 6}{6} + \frac{1}{6})$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{6 \cdot 6 + 1}{6}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $6$ by $6$ .

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{36 + 1}{6}$

Step 2.1.1.2.4.2

Add $36$ and $1$ .

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{37}{6}$

Step 2.2

Add $\frac{x}{5}$ to both sides of the equation.

$\frac{2 y}{3} = - \frac{37}{6} + \frac{x}{5}$

Step 2.3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

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 $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 2.4.1.1.1

Cancel the common factor of $3$ .

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Step 2.4.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Step 2.4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Step 2.4.1.1.2

Cancel the common factor of $2$ .

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Step 2.4.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Step 2.4.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $\frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$ .

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Step 2.4.2.1.1

Apply the distributive property.

$y = \frac{3}{2} (- \frac{37}{6}) + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.2

Cancel the common factor of $3$ .

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Step 2.4.2.1.2.1

Move the leading negative in $- \frac{37}{6}$ into the numerator.

$y = \frac{3}{2} \cdot \frac{- 37}{6} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.2.2

Factor $3$ out of $6$ .

$y = \frac{3}{2} \cdot \frac{- 37}{3 (2)} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.2.3

Cancel the common factor.

$y = \frac{3}{2} \cdot \frac{- 37}{3 \cdot 2} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.2.4

Rewrite the expression.

$y = \frac{1}{2} \cdot \frac{- 37}{2} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.3

Multiply $\frac{1}{2}$ by $\frac{- 37}{2}$ .

$y = \frac{- 37}{2 \cdot 2} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.4

Multiply $2$ by $2$ .

$y = \frac{- 37}{4} + \frac{3}{2} \cdot \frac{x}{5}$

Step 2.4.2.1.5

Multiply $\frac{3}{2} \cdot \frac{x}{5}$ .

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Step 2.4.2.1.5.1

Multiply $\frac{3}{2}$ by $\frac{x}{5}$ .

$y = \frac{- 37}{4} + \frac{3 x}{2 \cdot 5}$

Step 2.4.2.1.5.2

Multiply $2$ by $5$ .

$y = \frac{- 37}{4} + \frac{3 x}{10}$

Step 2.4.2.1.6

Move the negative in front of the fraction.

$y = - \frac{37}{4} + \frac{3 x}{10}$

Step 2.5

Reorder $- \frac{37}{4}$ and $\frac{3 x}{10}$ .

$y = \frac{3 x}{10} - \frac{37}{4}$

Step 2.6

Reorder terms.

$y = \frac{3}{10} x - \frac{37}{4}$