Algebra Examples

2 x - 3 y = 6

$2 x - 3 y = 6$

Step 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 2

Rewrite in slope-intercept form.

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Step 2.1

Subtract

2 x

$2 x$ from both sides of the equation.

- 3 y = 6 - 2 x

$- 3 y = 6 - 2 x$

Step 2.2

Divide each term in

- 3 y = 6 - 2 x

$- 3 y = 6 - 2 x$ by

- 3

$- 3$ and simplify.

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Step 2.2.1

Divide each term in

- 3 y = 6 - 2 x

$- 3 y = 6 - 2 x$ by

- 3

$- 3$ .

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

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

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

Step 2.2.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

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

6

$6$ by

- 3

$- 3$ .

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

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

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

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

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

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

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

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

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

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

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

Step 2.3

Write in

y = m x + b

$y = m x + b$ form.

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Step 2.3.1

Reorder

- 2

$- 2$ and

\frac{2 x}{3}

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

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

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

Step 2.3.2

Reorder terms.

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

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

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

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

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

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