Algebra Examples

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

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

Multiply both sides by $2$ .

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

Step 2.2

Simplify.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

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

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Factor $2$ out of $4$ .

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

Step 2.2.2.1.2

Cancel the common factor.

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

Step 2.2.2.1.3

Rewrite the expression.

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

Step 2.3

Solve for $y$ .

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Step 2.3.1

Simplify $\frac{x - 1}{2}$ .

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Step 2.3.1.1

Split the fraction $\frac{x - 1}{2}$ into two fractions.

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

Step 2.3.2

Subtract $x$ from both sides of the equation.

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

Step 2.3.3

Divide each term in $- 2 y = \frac{x}{2} - \frac{1}{2} - x$ by $- 2$ and simplify.

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Step 2.3.3.1

Divide each term in $- 2 y = \frac{x}{2} - \frac{1}{2} - x$ by $- 2$ .

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

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Cancel the common factor of $- 2$ .

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Step 2.3.3.2.1.1

Cancel the common factor.

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

Step 2.3.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.3.3.3

Simplify the right side.

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Step 2.3.3.3.1

Simplify each term.

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Step 2.3.3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.3.1.2

Move the negative in front of the fraction.

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

Step 2.3.3.3.1.3

Multiply $\frac{x}{2} (- \frac{1}{2})$ .

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Step 2.3.3.3.1.3.1

Multiply $\frac{x}{2}$ by $\frac{1}{2}$ .

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

Step 2.3.3.3.1.3.2

Multiply $2$ by $2$ .

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

Step 2.3.3.3.1.4

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.3.1.5

Move the negative in front of the fraction.

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

Step 2.3.3.3.1.6

Multiply $- \frac{1}{2} (- \frac{1}{2})$ .

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Step 2.3.3.3.1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.3.3.1.6.2

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

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

Step 2.3.3.3.1.6.3

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

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

Step 2.3.3.3.1.6.4

Multiply $2$ by $2$ .

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

Step 2.3.3.3.1.7

Dividing two negative values results in a positive value.

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

Step 2.4

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

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Step 2.4.1

Simplify $- \frac{x}{4} + \frac{1}{4} + \frac{x}{2}$ .

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Step 2.4.1.1

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.4.1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1.2.1

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

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

Step 2.4.1.2.2

Multiply $2$ by $2$ .

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

Step 2.4.1.3

Simplify terms.

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Step 2.4.1.3.1

Combine the numerators over the common denominator.

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

Step 2.4.1.3.2

Combine the numerators over the common denominator.

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

Step 2.4.1.4

Move $2$ to the left of $x$ .

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

Step 2.4.1.5

Add $- x$ and $2 x$ .

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

Step 2.4.2

Split the fraction $\frac{x + 1}{4}$ into two fractions.

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

Step 2.4.3

Reorder terms.

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