Algebra Examples

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

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 $2$ .

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

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.

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

Step 2.2.1.1.2

Rewrite the expression.

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

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 $4$ .

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

Step 2.2.2.1.2

Cancel the common factor.

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

Step 2.2.2.1.3

Rewrite the expression.

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

Step 2.3

Solve for $y$ .

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Step 2.3.1

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

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Step 2.3.1.1

Split the fraction $\frac{x - 4}{2}$ into two fractions.

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

Step 2.3.1.2

Divide $- 4$ by $2$ .

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

Step 2.3.2

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

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

Step 2.3.3

Divide each term in $- 2 y = \frac{x}{2} - 2 - 5 x$ by $- 2$ and simplify.

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Step 2.3.3.1

Divide each term in $- 2 y = \frac{x}{2} - 2 - 5 x$ by $- 2$ .

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

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.

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

Step 2.3.3.2.1.2

Divide $y$ by $1$ .

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

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.

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

Step 2.3.3.3.1.2

Move the negative in front of the fraction.

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

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 $\frac{1}{2}$ .

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

Step 2.3.3.3.1.3.2

Multiply $2$ by $2$ .

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

Step 2.3.3.3.1.4

Divide $- 2$ by $- 2$ .

$y = - \frac{x}{4} + 1 + \frac{- 5 x}{- 2}$

Step 2.3.3.3.1.5

Dividing two negative values results in a positive value.

$y = - \frac{x}{4} + 1 + \frac{5 x}{2}$

Step 2.4

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

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Step 2.4.1

Simplify $- \frac{x}{4} + 1 + \frac{5 x}{2}$ .

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Step 2.4.1.1

To write $\frac{5 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{x}{4} + \frac{5 x}{2} \cdot \frac{2}{2} + 1$

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

$y = - \frac{x}{4} + \frac{5 x \cdot 2}{2 \cdot 2} + 1$

Step 2.4.1.2.2

Multiply $2$ by $2$ .

$y = - \frac{x}{4} + \frac{5 x \cdot 2}{4} + 1$

Step 2.4.1.3

Combine the numerators over the common denominator.

$y = \frac{- x + 5 x \cdot 2}{4} + 1$

Step 2.4.1.4

Simplify each term.

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Step 2.4.1.4.1

Simplify the numerator.

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Step 2.4.1.4.1.1

Factor $x$ out of $- x + 5 x \cdot 2$ .

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Step 2.4.1.4.1.1.1

Factor $x$ out of $- x$ .

$y = \frac{x \cdot - 1 + 5 x \cdot 2}{4} + 1$

Step 2.4.1.4.1.1.2

Factor $x$ out of $5 x \cdot 2$ .

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

Step 2.4.1.4.1.1.3

Factor $x$ out of $x \cdot - 1 + x (5 \cdot 2)$ .

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

Step 2.4.1.4.1.2

Multiply $5$ by $2$ .

$y = \frac{x (- 1 + 10)}{4} + 1$

Step 2.4.1.4.1.3

Add $- 1$ and $10$ .

$y = \frac{x \cdot 9}{4} + 1$

Step 2.4.1.4.2

Move $9$ to the left of $x$ .

$y = \frac{9 x}{4} + 1$

Step 2.4.2

Reorder terms.

$y = \frac{9}{4} x + 1$