Algebra Examples

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

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 left side.

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Step 2.1.1

Simplify $3 x - 3 (x + 2)$ .

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Apply the distributive property.

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

Step 2.1.1.1.2

Multiply $- 3$ by $2$ .

$3 x - 3 x - 6 = 2 y - 3 x$

Step 2.1.1.2

Simplify by adding terms.

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Step 2.1.1.2.1

Subtract $3 x$ from $3 x$ .

$0 - 6 = 2 y - 3 x$

Step 2.1.1.2.2

Subtract $6$ from $0$ .

$- 6 = 2 y - 3 x$

Step 2.2

Rewrite the equation as $2 y - 3 x = - 6$ .

$2 y - 3 x = - 6$

Step 2.3

Add $3 x$ to both sides of the equation.

$2 y = - 6 + 3 x$

Step 2.4

Divide each term in $2 y = - 6 + 3 x$ by $2$ and simplify.

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Step 2.4.1

Divide each term in $2 y = - 6 + 3 x$ by $2$ .

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

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.1.1

Cancel the common factor.

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

Step 2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 6$ by $2$ .

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

Step 2.5

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

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Step 2.5.1

Reorder $- 3$ and $\frac{3 x}{2}$ .

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

Step 2.5.2

Reorder terms.

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