Pre-Algebra Examples

$\frac{1}{6} x - \frac{1}{3} y = - 10$

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

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{6} - \frac{1}{3} y = - 10$

Step 1.2.1.2

Combine $y$ and $\frac{1}{3}$ .

$\frac{x}{6} - \frac{y}{3} = - 10$

Step 1.3

Subtract $\frac{x}{6}$ from both sides of the equation.

$- \frac{y}{3} = - 10 - \frac{x}{6}$

Step 1.4

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{y}{3}) = - 3 (- 10 - \frac{x}{6})$

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 1.5.1.1.1

Cancel the common factor of $3$ .

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Step 1.5.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 3 \frac{- y}{3} = - 3 (- 10 - \frac{x}{6})$

Step 1.5.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 (- 10 - \frac{x}{6})$

Step 1.5.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- y}{3} = - 3 (- 10 - \frac{x}{6})$

Step 1.5.1.1.1.4

Rewrite the expression.

$- - y = - 3 (- 10 - \frac{x}{6})$

Step 1.5.1.1.2

Multiply.

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Step 1.5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 (- 10 - \frac{x}{6})$

Step 1.5.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 (- 10 - \frac{x}{6})$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $- 3 (- 10 - \frac{x}{6})$ .

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Step 1.5.2.1.1

Simplify terms.

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Step 1.5.2.1.1.1

Apply the distributive property.

$y = - 3 \cdot - 10 - 3 (- \frac{x}{6})$

Step 1.5.2.1.1.2

Multiply $- 3$ by $- 10$ .

$y = 30 - 3 (- \frac{x}{6})$

Step 1.5.2.1.1.3

Cancel the common factor of $3$ .

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Step 1.5.2.1.1.3.1

Move the leading negative in $- \frac{x}{6}$ into the numerator.

$y = 30 - 3 \frac{- x}{6}$

Step 1.5.2.1.1.3.2

Factor $3$ out of $- 3$ .

$y = 30 + 3 (- 1) \frac{- x}{6}$

Step 1.5.2.1.1.3.3

Factor $3$ out of $6$ .

$y = 30 + 3 \cdot - 1 \frac{- x}{3 \cdot 2}$

Step 1.5.2.1.1.3.4

Cancel the common factor.

$y = 30 + 3 \cdot - 1 \frac{- x}{3 \cdot 2}$

Step 1.5.2.1.1.3.5

Rewrite the expression.

$y = 30 - \frac{- x}{2}$

Step 1.5.2.1.2

Simplify each term.

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Step 1.5.2.1.2.1

Move the negative in front of the fraction.

$y = 30 - - \frac{x}{2}$

Step 1.5.2.1.2.2

Multiply $- - \frac{x}{2}$ .

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Step 1.5.2.1.2.2.1

Multiply $- 1$ by $- 1$ .

$y = 30 + 1 \frac{x}{2}$

Step 1.5.2.1.2.2.2

Multiply $\frac{x}{2}$ by $1$ .

$y = 30 + \frac{x}{2}$

Step 1.6

Reorder $30$ and $\frac{x}{2}$ .

$y = \frac{x}{2} + 30$

Step 1.7

Reorder terms.

$y = \frac{1}{2} x + 30$

Step 2

Using the slope-intercept form, the y-intercept is $30$ .

$b = 30$

Step 3

y-intercept in point form.

$(0, 30)$

Step 4