Algebra Examples

$\frac{x - y}{5} = \frac{x + y}{4} - 1$

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

Simplify $\frac{x + y}{4} - 1$ .

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Step 2.1.1.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x - y}{5} = \frac{x + y}{4} - 1 \cdot \frac{4}{4}$

Step 2.1.1.2

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{x - y}{5} = \frac{x + y}{4} + \frac{- 1 \cdot 4}{4}$

Step 2.1.1.3

Combine the numerators over the common denominator.

$\frac{x - y}{5} = \frac{x + y - 1 \cdot 4}{4}$

Step 2.1.1.4

Multiply $- 1$ by $4$ .

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

Step 2.2

Multiply both sides by $5$ .

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

Step 2.3

Simplify.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $5$ .

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Step 2.3.1.1.1

Cancel the common factor.

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

Step 2.3.1.1.2

Rewrite the expression.

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

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $\frac{x + y - 4}{4} \cdot 5$ .

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Step 2.3.2.1.1

Combine $\frac{x + y - 4}{4}$ and $5$ .

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

Step 2.3.2.1.2

Move $5$ to the left of $x + y - 4$ .

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

Step 2.4

Solve for $y$ .

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Step 2.4.1

Multiply both sides by $4$ .

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

Step 2.4.2

Simplify.

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Step 2.4.2.1

Simplify the left side.

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Step 2.4.2.1.1

Simplify $(x - y) \cdot 4$ .

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Step 2.4.2.1.1.1

Apply the distributive property.

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

Step 2.4.2.1.1.2

Simplify the expression.

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Step 2.4.2.1.1.2.1

Move $4$ to the left of $x$ .

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

Step 2.4.2.1.1.2.2

Multiply $4$ by $- 1$ .

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

Step 2.4.2.2

Simplify the right side.

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Step 2.4.2.2.1

Simplify $\frac{5 (x + y - 4)}{4} \cdot 4$ .

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Step 2.4.2.2.1.1

Cancel the common factor of $4$ .

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Step 2.4.2.2.1.1.1

Cancel the common factor.

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

Step 2.4.2.2.1.1.2

Rewrite the expression.

$4 x - 4 y = 5 (x + y - 4)$

Step 2.4.2.2.1.2

Apply the distributive property.

$4 x - 4 y = 5 x + 5 y + 5 \cdot - 4$

Step 2.4.2.2.1.3

Multiply $5$ by $- 4$ .

$4 x - 4 y = 5 x + 5 y - 20$

Step 2.4.3

Solve for $y$ .

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Step 2.4.3.1

Move all terms containing $y$ to the left side of the equation.

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Step 2.4.3.1.1

Subtract $5 y$ from both sides of the equation.

$4 x - 4 y - 5 y = 5 x - 20$

Step 2.4.3.1.2

Subtract $5 y$ from $- 4 y$ .

$4 x - 9 y = 5 x - 20$

Step 2.4.3.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.4.3.2.1

Subtract $4 x$ from both sides of the equation.

$- 9 y = 5 x - 20 - 4 x$

Step 2.4.3.2.2

Subtract $4 x$ from $5 x$ .

$- 9 y = x - 20$

Step 2.4.3.3

Divide each term in $- 9 y = x - 20$ by $- 9$ and simplify.

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Step 2.4.3.3.1

Divide each term in $- 9 y = x - 20$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{x}{- 9} + \frac{- 20}{- 9}$

Step 2.4.3.3.2

Simplify the left side.

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Step 2.4.3.3.2.1

Cancel the common factor of $- 9$ .

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Step 2.4.3.3.2.1.1

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{x}{- 9} + \frac{- 20}{- 9}$

Step 2.4.3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{- 9} + \frac{- 20}{- 9}$

Step 2.4.3.3.3

Simplify the right side.

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Step 2.4.3.3.3.1

Simplify each term.

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Step 2.4.3.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{x}{9} + \frac{- 20}{- 9}$

Step 2.4.3.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{x}{9} + \frac{20}{9}$

Step 2.5

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

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Step 2.5.1

Reorder terms.

$y = - (\frac{1}{9} x) + \frac{20}{9}$

Step 2.5.2

Remove parentheses.

$y = - \frac{1}{9} x + \frac{20}{9}$