Pre-Algebra Examples

3 x - 2 y + 6 = 0

$3 x - 2 y + 6 = 0$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 1.2.1

Subtract

3 x

$3 x$ from both sides of the equation.

- 2 y + 6 = - 3 x

$- 2 y + 6 = - 3 x$

Step 1.2.2

Subtract

6

$6$ from both sides of the equation.

- 2 y = - 3 x - 6

$- 2 y = - 3 x - 6$

- 2 y = - 3 x - 6

$- 2 y = - 3 x - 6$

Step 1.3

Divide each term in

- 2 y = - 3 x - 6

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

- 2

$- 2$ and simplify.

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Step 1.3.1

Divide each term in

- 2 y = - 3 x - 6

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

- 2

$- 2$ .

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Dividing two negative values results in a positive value.

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

Step 1.3.3.1.2

Divide

$- 6$ by

$- 2$ .

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

Step 1.4

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is

$\frac{3}{2}$ .

$m = \frac{3}{2}$

Step 3