Algebra Examples

$\frac{4 x - 3 y}{3} = \frac{2 x - 3}{6}$

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

Multiply both sides by $3$ .

$\frac{4 x - 3 y}{3} \cdot 3 = \frac{2 x - 3}{6} \cdot 3$

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 $3$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{4 x - 3 y}{3} \cdot 3 = \frac{2 x - 3}{6} \cdot 3$

Step 2.2.1.1.2

Rewrite the expression.

$4 x - 3 y = \frac{2 x - 3}{6} \cdot 3$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Factor $3$ out of $6$ .

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

Step 2.2.2.1.2

Cancel the common factor.

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

Step 2.2.2.1.3

Rewrite the expression.

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

Step 2.3

Solve for $y$ .

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Step 2.3.1

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

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Step 2.3.1.1

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

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

Step 2.3.1.2

Simplify each term.

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Step 2.3.1.2.1

Cancel the common factor of $2$ .

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Step 2.3.1.2.1.1

Cancel the common factor.

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

Step 2.3.1.2.1.2

Divide $x$ by $1$ .

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

Step 2.3.1.2.2

Move the negative in front of the fraction.

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

Subtract $4 x$ from $x$ .

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

Step 2.3.3

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

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Step 2.3.3.1

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

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

Step 2.3.3.2

Simplify the left side.

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Step 2.3.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.3.2.1.1

Cancel the common factor.

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

Step 2.3.3.2.1.2

Divide $y$ by $1$ .

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

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

Cancel the common factor of $- 3$ .

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Step 2.3.3.3.1.1.1

Cancel the common factor.

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

Step 2.3.3.3.1.1.2

Divide $x$ by $1$ .

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

Step 2.3.3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.3.3.1.3

Cancel the common factor of $3$ .

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Step 2.3.3.3.1.3.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 2.3.3.3.1.3.2

Factor $3$ out of $- 3$ .

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

Step 2.3.3.3.1.3.3

Factor $3$ out of $- 3$ .

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

Step 2.3.3.3.1.3.4

Cancel the common factor.

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

Step 2.3.3.3.1.3.5

Rewrite the expression.

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

Step 2.3.3.3.1.4

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

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

Step 2.3.3.3.1.5

Multiply $2$ by $- 1$ .

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

Step 2.3.3.3.1.6

Dividing two negative values results in a positive value.

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