Algebra Examples

$5 x - 12 = 9 (2 y - 1)$

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 $9 (2 y - 1)$ .

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Step 2.1.1.1

Apply the distributive property.

$5 x - 12 = 9 (2 y) + 9 \cdot - 1$

Step 2.1.1.2

Multiply.

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Step 2.1.1.2.1

Multiply $2$ by $9$ .

$5 x - 12 = 18 y + 9 \cdot - 1$

Step 2.1.1.2.2

Multiply $9$ by $- 1$ .

$5 x - 12 = 18 y - 9$

Step 2.2

Rewrite the equation as $18 y - 9 = 5 x - 12$ .

$18 y - 9 = 5 x - 12$

Step 2.3

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

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Step 2.3.1

Add $9$ to both sides of the equation.

$18 y = 5 x - 12 + 9$

Step 2.3.2

Add $- 12$ and $9$ .

$18 y = 5 x - 3$

Step 2.4

Divide each term in $18 y = 5 x - 3$ by $18$ and simplify.

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Step 2.4.1

Divide each term in $18 y = 5 x - 3$ by $18$ .

$\frac{18 y}{18} = \frac{5 x}{18} + \frac{- 3}{18}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $18$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{18 y}{18} = \frac{5 x}{18} + \frac{- 3}{18}$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{5 x}{18} + \frac{- 3}{18}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

Cancel the common factor of $- 3$ and $18$ .

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Step 2.4.3.1.1.1

Factor $3$ out of $- 3$ .

$y = \frac{5 x}{18} + \frac{3 (- 1)}{18}$

Step 2.4.3.1.1.2

Cancel the common factors.

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Step 2.4.3.1.1.2.1

Factor $3$ out of $18$ .

$y = \frac{5 x}{18} + \frac{3 \cdot - 1}{3 \cdot 6}$

Step 2.4.3.1.1.2.2

Cancel the common factor.

$y = \frac{5 x}{18} + \frac{3 \cdot - 1}{3 \cdot 6}$

Step 2.4.3.1.1.2.3

Rewrite the expression.

$y = \frac{5 x}{18} + \frac{- 1}{6}$

Step 2.4.3.1.2

Move the negative in front of the fraction.

$y = \frac{5 x}{18} - \frac{1}{6}$

Step 2.5

Reorder terms.

$y = \frac{5}{18} x - \frac{1}{6}$