Write in Slope-Intercept Form

$6 x - 3 y = 12$

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

Subtract $6 x$ from both sides of the equation.

$- 3 y = 12 - 6 x$

Step 2.2

Divide each term in $- 3 y = 12 - 6 x$ by $- 3$ and simplify.

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Step 2.2.1

Divide each term in $- 3 y = 12 - 6 x$ by $- 3$ .

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

Step 2.2.2

Simplify the left 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

Cancel the common factor.

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

Step 2.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $12$ by $- 3$ .

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

Step 2.2.3.1.2

Cancel the common factor of $- 6$ and $- 3$ .

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Step 2.2.3.1.2.1

Factor $- 3$ out of $- 6 x$ .

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

Step 2.2.3.1.2.2

Cancel the common factors.

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Step 2.2.3.1.2.2.1

Factor $- 3$ out of $- 3$ .

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

Step 2.2.3.1.2.2.2

Cancel the common factor.

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

Step 2.2.3.1.2.2.3

Rewrite the expression.

$y = - 4 + \frac{2 x}{1}$

Step 2.2.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - 4 + 2 x$

Step 2.3

Reorder $- 4$ and $2 x$ .

$y = 2 x - 4$

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