Finite Math Examples

$\frac{1}{2} x - \frac{2}{3} y = 12$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$\frac{1}{2} x - \frac{2}{3} \cdot 0 = 12$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $\frac{1}{2} x - \frac{2}{3} \cdot 0$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

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

$\frac{x}{2} - \frac{2}{3} \cdot 0 = 12$

Step 1.2.1.1.2

Multiply $- \frac{2}{3} \cdot 0$ .

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Step 1.2.1.1.2.1

Multiply $0$ by $- 1$ .

$\frac{x}{2} + 0 (\frac{2}{3}) = 12$

Step 1.2.1.1.2.2

Multiply $0$ by $\frac{2}{3}$ .

$\frac{x}{2} + 0 = 12$

Step 1.2.1.2

Add $\frac{x}{2}$ and $0$ .

$\frac{x}{2} = 12$

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 12$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 12$

Step 1.2.3.1.1.2

Rewrite the expression.

$x = 2 \cdot 12$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $2$ by $12$ .

$x = 24$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(24, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$\frac{1}{2} \cdot (0) - \frac{2}{3} y = 12$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $\frac{1}{2} \cdot (0) - \frac{2}{3} y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Multiply $\frac{1}{2}$ by $0$ .

$0 - \frac{2}{3} y = 12$

Step 2.2.1.1.2

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

$0 - \frac{y \cdot 2}{3} = 12$

Step 2.2.1.1.3

Move $2$ to the left of $y$ .

$0 - \frac{2 y}{3} = 12$

Step 2.2.1.2

Subtract $\frac{2 y}{3}$ from $0$ .

$- \frac{2 y}{3} = 12$

Step 2.2.2

Multiply both sides of the equation by $- \frac{3}{2}$ .

$- \frac{3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot 12$

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

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

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Step 2.2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- 3}{2} (- \frac{2 y}{3}) = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.1.2

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

$\frac{- 3}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{2} \cdot \frac{- 2 y}{3} = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 y) = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.3.1.1.2.1

Factor $2$ out of $- 2 y$ .

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- y)) = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.2.3

Rewrite the expression.

$- - y = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.3

Multiply.

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Step 2.2.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{2} \cdot 12$

Step 2.2.3.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{2} \cdot 12$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Simplify $- \frac{3}{2} \cdot 12$ .

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Step 2.2.3.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.3.2.1.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$y = \frac{- 3}{2} \cdot 12$

Step 2.2.3.2.1.1.2

Factor $2$ out of $12$ .

$y = \frac{- 3}{2} \cdot (2 (6))$

Step 2.2.3.2.1.1.3

Cancel the common factor.

$y = \frac{- 3}{2} \cdot (2 \cdot 6)$

Step 2.2.3.2.1.1.4

Rewrite the expression.

$y = - 3 \cdot 6$

Step 2.2.3.2.1.2

Multiply $- 3$ by $6$ .

$y = - 18$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 18)$

Step 3

List the intersections.

x-intercept(s): $(24, 0)$

y-intercept(s): $(0, - 18)$

Step 4