Pre-Algebra Examples

$x - 3 y - 9 = 0$

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

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Subtract $x$ from both sides of the equation.

$- 3 y - 9 = - x$

Step 1.2.2

Add $9$ to both sides of the equation.

$- 3 y = - x + 9$

Step 1.3

Divide each term in $- 3 y = - x + 9$ by $- 3$ and simplify.

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Step 1.3.1

Divide each term in $- 3 y = - x + 9$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- x}{- 3} + \frac{9}{- 3}$

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.

$\frac{- 3 y}{- 3} = \frac{- x}{- 3} + \frac{9}{- 3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x}{- 3} + \frac{9}{- 3}$

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

Dividing two negative values results in a positive value.

$y = \frac{x}{3} + \frac{9}{- 3}$

Step 1.3.3.1.2

Divide $9$ by $- 3$ .

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

Step 1.4

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{1}{3}$ .

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

Step 3