Finite Math Examples

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

Step 1

Write $f (x) = - \frac{2}{3} x$ as an equation.

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

Step 2

Simplify $- \frac{2}{3} x$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Cancel the common factor of $0$ and $3$ .

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Step 4.2.1.1

Factor $3$ out of $2 (0)$ .

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

Step 4.2.1.2

Cancel the common factors.

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Step 4.2.1.2.1

Factor $3$ out of $3$ .

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

Step 4.2.1.2.2

Cancel the common factor.

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

Step 4.2.1.2.3

Rewrite the expression.

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

Step 4.2.1.2.4

Divide $2 \cdot (0)$ by $1$ .

$y = - (2 \cdot (0))$

Step 4.2.2

Multiply $- (2 \cdot (0))$ .

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Step 4.2.2.1

Multiply $2$ by $0$ .

$y = - 0$

Step 4.2.2.2

Multiply $- 1$ by $0$ .

$y = 0$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, 0)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

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

Step 5.2

Multiply $2$ by $1$ .

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

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{2}{3})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

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

Step 6.2

Multiply $2$ by $2$ .

$y = - \frac{4}{3}$

Step 6.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{4}{3})$

Step 7

These are three possible solutions to the equation.

$(0, 0), (1, - \frac{2}{3}), (2, - \frac{4}{3})$

Step 8