Algebra Examples

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

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

Cancel the common factor of $3 x - 3$ and $6$ .

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Step 2.1.1.1

Factor $3$ out of $3 x$ .

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

Step 2.1.1.2

Factor $3$ out of $- 3$ .

$\frac{4 x - y}{3} = \frac{3 (x) + 3 (- 1)}{6}$

Step 2.1.1.3

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\frac{4 x - y}{3} = \frac{3 (x - 1)}{6}$

Step 2.1.1.4

Cancel the common factors.

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Step 2.1.1.4.1

Factor $3$ out of $6$ .

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

Step 2.1.1.4.2

Cancel the common factor.

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

Step 2.1.1.4.3

Rewrite the expression.

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

Step 2.2

Multiply both sides by $3$ .

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

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

Cancel the common factor of $3$ .

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Step 2.3.1.1.1

Cancel the common factor.

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

Step 2.3.1.1.2

Rewrite the expression.

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

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

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

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Step 2.3.2.1.1

Combine $\frac{x - 1}{2}$ and $3$ .

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

Step 2.3.2.1.2

Move $3$ to the left of $x - 1$ .

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

Step 2.4

Solve for $y$ .

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Step 2.4.1

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

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

Step 2.4.2

Divide each term in $- y = \frac{3 (x - 1)}{2} - 4 x$ by $- 1$ and simplify.

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Step 2.4.2.1

Divide each term in $- y = \frac{3 (x - 1)}{2} - 4 x$ by $- 1$ .

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

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Dividing two negative values results in a positive value.

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

Step 2.4.2.2.2

Divide $y$ by $1$ .

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

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Combine the numerators over the common denominator.

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

Step 2.4.2.3.2

Simplify the expression.

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Step 2.4.2.3.2.1

Move the negative one from the denominator of $\frac{\frac{3 (x - 1)}{2} - 4 x}{- 1}$ .

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

Step 2.4.2.3.2.2

Rewrite $- 1 \cdot (\frac{3 (x - 1)}{2} - 4 x)$ as $- (\frac{3 (x - 1)}{2} - 4 x)$ .

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

Step 2.4.2.3.3

Apply the distributive property.

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

Step 2.4.2.3.4

Multiply $- 4$ by $- 1$ .

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

Step 2.5

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

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Step 2.5.1

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

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Step 2.5.1.1

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.5.1.2

Simplify terms.

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Step 2.5.1.2.1

Combine $4 x$ and $\frac{2}{2}$ .

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

Step 2.5.1.2.2

Combine the numerators over the common denominator.

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

Step 2.5.1.3

Simplify the numerator.

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Step 2.5.1.3.1

Apply the distributive property.

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

Step 2.5.1.3.2

Multiply $- 3$ by $- 1$ .

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

Step 2.5.1.3.3

Multiply $2$ by $4$ .

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

Step 2.5.1.3.4

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

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

Step 2.5.2

Split the fraction $\frac{5 x + 3}{2}$ into two fractions.

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

Step 2.5.3

Reorder terms.

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