Algebra Examples

$2 x - 3 y = 6$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Subtract

$2 x$ from both sides of the equation.

$- 3 y = 6 - 2 x$

Step 1.3

Divide each term in

$- 3 y = 6 - 2 x$ by

$- 3$ and simplify.

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Step 1.3.1

Divide each term in

$- 3 y = 6 - 2 x$ by

$- 3$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

$- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

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

Divide

$6$ by

$- 3$ .

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

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$- 2$ and

$\frac{2 x}{3}$ .

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

Step 1.4.2

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is

$\frac{2}{3}$ .

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

Step 3