Finite Math Examples

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

Step 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 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2.1.1.2

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

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

Step 2.2

Subtract $\frac{x}{2}$ from both sides of the equation.

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

Step 2.3

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

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

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

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

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Step 2.4.1.1.1

Cancel the common factor of $3$ .

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Step 2.4.1.1.1.1

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

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

Step 2.4.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.4.1.1.1.3

Cancel the common factor.

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

Step 2.4.1.1.1.4

Rewrite the expression.

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

Step 2.4.1.1.2

Multiply.

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Step 2.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.4.1.1.2.2

Multiply $y$ by $1$ .

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

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $- 3 (- 1 - \frac{x}{2})$ .

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Step 2.4.2.1.1

Apply the distributive property.

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

Step 2.4.2.1.2

Multiply $- 3$ by $- 1$ .

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

Step 2.4.2.1.3

Multiply $- 3 (- \frac{x}{2})$ .

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Step 2.4.2.1.3.1

Multiply $- 1$ by $- 3$ .

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

Step 2.4.2.1.3.2

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

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

Step 2.5

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

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

Step 2.6

Reorder terms.

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