Algebra Examples

$\frac{4 x - 4 y}{3} = \frac{3 x - 4}{6}$

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 left side.

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Step 2.1.1

Factor $4$ out of $4 x - 4 y$ .

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Step 2.1.1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 4 y}{3} = \frac{3 x - 4}{6}$

Step 2.1.1.2

Factor $4$ out of $- 4 y$ .

$\frac{4 (x) + 4 (- y)}{3} = \frac{3 x - 4}{6}$

Step 2.1.1.3

Factor $4$ out of $4 (x) + 4 (- y)$ .

$\frac{4 (x - y)}{3} = \frac{3 x - 4}{6}$

Step 2.2

Multiply both sides by $3$ .

$\frac{4 (x - y)}{3} \cdot 3 = \frac{3 x - 4}{6} \cdot 3$

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

Simplify $\frac{4 (x - y)}{3} \cdot 3$ .

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Step 2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.3.1.1.1.1

Cancel the common factor.

$\frac{4 (x - y)}{3} \cdot 3 = \frac{3 x - 4}{6} \cdot 3$

Step 2.3.1.1.1.2

Rewrite the expression.

$4 (x - y) = \frac{3 x - 4}{6} \cdot 3$

Step 2.3.1.1.2

Apply the distributive property.

$4 x + 4 (- y) = \frac{3 x - 4}{6} \cdot 3$

Step 2.3.1.1.3

Multiply $- 1$ by $4$ .

$4 x - 4 y = \frac{3 x - 4}{6} \cdot 3$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Factor $3$ out of $6$ .

$4 x - 4 y = \frac{3 x - 4}{3 (2)} \cdot 3$

Step 2.3.2.1.2

Cancel the common factor.

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

Step 2.3.2.1.3

Rewrite the expression.

$4 x - 4 y = \frac{3 x - 4}{2}$

Step 2.4

Solve for $y$ .

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Step 2.4.1

Simplify $\frac{3 x - 4}{2}$ .

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Step 2.4.1.1

Split the fraction $\frac{3 x - 4}{2}$ into two fractions.

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

Step 2.4.1.2

Divide $- 4$ by $2$ .

$4 x - 4 y = \frac{3 x}{2} - 2$

Step 2.4.2

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

$- 4 y = \frac{3 x}{2} - 2 - 4 x$

Step 2.4.3

Divide each term in $- 4 y = \frac{3 x}{2} - 2 - 4 x$ by $- 4$ and simplify.

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Step 2.4.3.1

Divide each term in $- 4 y = \frac{3 x}{2} - 2 - 4 x$ by $- 4$ .

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

Step 2.4.3.2

Simplify the left side.

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Step 2.4.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.4.3.2.1.1

Cancel the common factor.

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

Step 2.4.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.3.3

Simplify the right side.

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Step 2.4.3.3.1

Simplify each term.

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Step 2.4.3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3 x}{2} \cdot \frac{1}{- 4} + \frac{- 2}{- 4} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.2

Move the negative in front of the fraction.

$y = \frac{3 x}{2} (- \frac{1}{4}) + \frac{- 2}{- 4} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.3

Multiply $\frac{3 x}{2} (- \frac{1}{4})$ .

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Step 2.4.3.3.1.3.1

Multiply $\frac{3 x}{2}$ by $\frac{1}{4}$ .

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

Step 2.4.3.3.1.3.2

Multiply $2$ by $4$ .

$y = - \frac{3 x}{8} + \frac{- 2}{- 4} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.4

Cancel the common factor of $- 2$ and $- 4$ .

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Step 2.4.3.3.1.4.1

Factor $- 2$ out of $- 2$ .

$y = - \frac{3 x}{8} + \frac{- 2 (1)}{- 4} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.4.2

Cancel the common factors.

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Step 2.4.3.3.1.4.2.1

Factor $- 2$ out of $- 4$ .

$y = - \frac{3 x}{8} + \frac{- 2 \cdot 1}{- 2 \cdot 2} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.4.2.2

Cancel the common factor.

$y = - \frac{3 x}{8} + \frac{- 2 \cdot 1}{- 2 \cdot 2} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.4.2.3

Rewrite the expression.

$y = - \frac{3 x}{8} + \frac{1}{2} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.5

Cancel the common factor of $- 4$ .

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Step 2.4.3.3.1.5.1

Cancel the common factor.

$y = - \frac{3 x}{8} + \frac{1}{2} + \frac{- 4 x}{- 4}$

Step 2.4.3.3.1.5.2

Divide $x$ by $1$ .

$y = - \frac{3 x}{8} + \frac{1}{2} + x$

Step 2.5

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

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Step 2.5.1

Simplify $- \frac{3 x}{8} + \frac{1}{2} + x$ .

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Step 2.5.1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = - \frac{3 x}{8} + x \cdot \frac{8}{8} + \frac{1}{2}$

Step 2.5.1.2

Combine $x$ and $\frac{8}{8}$ .

$y = - \frac{3 x}{8} + \frac{x \cdot 8}{8} + \frac{1}{2}$

Step 2.5.1.3

Combine the numerators over the common denominator.

$y = \frac{- 3 x + x \cdot 8}{8} + \frac{1}{2}$

Step 2.5.1.4

Add $- 3 x$ and $x \cdot 8$ .

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Step 2.5.1.4.1

Reorder $x$ and $8$ .

$y = \frac{- 3 x + 8 \cdot x}{8} + \frac{1}{2}$

Step 2.5.1.4.2

Add $- 3 x$ and $8 \cdot x$ .

$y = \frac{5 x}{8} + \frac{1}{2}$

Step 2.5.2

Reorder terms.

$y = \frac{5}{8} x + \frac{1}{2}$