Algebra Examples

$12 y = \frac{8 x - 48}{3}$

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

Factor $8$ out of $8 x - 48$ .

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Step 2.1.1.1

Factor $8$ out of $8 x$ .

$12 y = \frac{8 (x) - 48}{3}$

Step 2.1.1.2

Factor $8$ out of $- 48$ .

$12 y = \frac{8 x + 8 \cdot - 6}{3}$

Step 2.1.1.3

Factor $8$ out of $8 x + 8 \cdot - 6$ .

$12 y = \frac{8 (x - 6)}{3}$

Step 2.2

Divide each term in $12 y = \frac{8 (x - 6)}{3}$ by $12$ and simplify.

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Step 2.2.1

Divide each term in $12 y = \frac{8 (x - 6)}{3}$ by $12$ .

$\frac{12 y}{12} = \frac{\frac{8 (x - 6)}{3}}{12}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $12$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{12 y}{12} = \frac{\frac{8 (x - 6)}{3}}{12}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{8 (x - 6)}{3}}{12}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{8 (x - 6)}{3} \cdot \frac{1}{12}$

Step 2.2.3.2

Cancel the common factor of $4$ .

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Step 2.2.3.2.1

Factor $4$ out of $8 (x - 6)$ .

$y = \frac{4 (2 (x - 6))}{3} \cdot \frac{1}{12}$

Step 2.2.3.2.2

Factor $4$ out of $12$ .

$y = \frac{4 (2 (x - 6))}{3} \cdot \frac{1}{4 (3)}$

Step 2.2.3.2.3

Cancel the common factor.

$y = \frac{4 (2 (x - 6))}{3} \cdot \frac{1}{4 \cdot 3}$

Step 2.2.3.2.4

Rewrite the expression.

$y = \frac{2 (x - 6)}{3} \cdot \frac{1}{3}$

Step 2.2.3.3

Multiply $\frac{2 (x - 6)}{3}$ by $\frac{1}{3}$ .

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

Step 2.2.3.4

Multiply $3$ by $3$ .

$y = \frac{2 (x - 6)}{9}$

Step 2.3

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

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Step 2.3.1

Apply the distributive property.

$y = \frac{2 x + 2 \cdot - 6}{9}$

Step 2.3.2

Multiply $2$ by $- 6$ .

$y = \frac{2 x - 12}{9}$

Step 2.3.3

Split the fraction $\frac{2 x - 12}{9}$ into two fractions.

$y = \frac{2 x}{9} + \frac{- 12}{9}$

Step 2.3.4

Cancel the common factor of $- 12$ and $9$ .

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Step 2.3.4.1

Factor $3$ out of $- 12$ .

$y = \frac{2 x}{9} + \frac{3 (- 4)}{9}$

Step 2.3.4.2

Cancel the common factors.

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Step 2.3.4.2.1

Factor $3$ out of $9$ .

$y = \frac{2 x}{9} + \frac{3 \cdot - 4}{3 \cdot 3}$

Step 2.3.4.2.2

Cancel the common factor.

$y = \frac{2 x}{9} + \frac{3 \cdot - 4}{3 \cdot 3}$

Step 2.3.4.2.3

Rewrite the expression.

$y = \frac{2 x}{9} + \frac{- 4}{3}$

Step 2.3.5

Move the negative in front of the fraction.

$y = \frac{2 x}{9} - \frac{4}{3}$

Step 2.3.6

Reorder terms.

$y = \frac{2}{9} x - \frac{4}{3}$