Algebra Examples

x - 3 y = 6

$x - 3 y = 6$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Subtract

x

$x$ from both sides of the equation.

- 3 y = 6 - x

$- 3 y = 6 - x$

Step 1.3

Divide each term in

- 3 y = 6 - x

$- 3 y = 6 - x$ by

- 3

$- 3$ and simplify.

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Step 1.3.1

Divide each term in

- 3 y = 6 - x

$- 3 y = 6 - x$ by

- 3

$- 3$ .

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

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

$- 3$ .

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

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$- 2$ and

$\frac{x}{3}$ .

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

Step 1.4.2

Reorder terms.

$y = \frac{1}{3} x - 2$

Step 2

Using the slope-intercept form, the slope is

$\frac{1}{3}$ .

$m = \frac{1}{3}$

Step 3

$x - 3 y = 6$

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