Algebra Examples

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

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 right side.

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Step 2.1.1

Simplify $\frac{4 x - 4}{6}$ .

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Step 2.1.1.1

Cancel the common factor of $4 x - 4$ and $6$ .

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Step 2.1.1.1.1

Factor $2$ out of $4 x$ .

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

Step 2.1.1.1.2

Factor $2$ out of $- 4$ .

$\frac{3 x - y}{3} = \frac{2 (2 x) + 2 (- 2)}{6}$

Step 2.1.1.1.3

Factor $2$ out of $2 (2 x) + 2 (- 2)$ .

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

Step 2.1.1.1.4

Cancel the common factors.

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Step 2.1.1.1.4.1

Factor $2$ out of $6$ .

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

Step 2.1.1.1.4.2

Cancel the common factor.

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

Step 2.1.1.1.4.3

Rewrite the expression.

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

Factor $2$ out of $2 x$ .

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

Step 2.1.1.2.2

Factor $2$ out of $- 2$ .

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

Step 2.1.1.2.3

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

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

Step 2.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x - y = 2 (x - 1)$

Step 2.3

Simplify $2 (x - 1)$ .

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Step 2.3.1

Rewrite.

$3 x - y = 0 + 0 + 2 (x - 1)$

Step 2.3.2

Simplify by adding zeros.

$3 x - y = 2 (x - 1)$

Step 2.3.3

Apply the distributive property.

$3 x - y = 2 x + 2 \cdot - 1$

Step 2.3.4

Multiply $2$ by $- 1$ .

$3 x - y = 2 x - 2$

Step 2.4

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

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Step 2.4.1

Subtract $3 x$ from both sides of the equation.

$- y = 2 x - 2 - 3 x$

Step 2.4.2

Subtract $3 x$ from $2 x$ .

$- y = - x - 2$

Step 2.5

Divide each term in $- y = - x - 2$ by $- 1$ and simplify.

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Step 2.5.1

Divide each term in $- y = - x - 2$ by $- 1$ .

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

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Dividing two negative values results in a positive value.

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

Step 2.5.2.2

Divide $y$ by $1$ .

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

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Simplify each term.

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Step 2.5.3.1.1

Dividing two negative values results in a positive value.

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

Step 2.5.3.1.2

Divide $x$ by $1$ .

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

Step 2.5.3.1.3

Divide $- 2$ by $- 1$ .

$y = x + 2$