Algebra Examples

$h (x) = \frac{2}{3} x - 4$

Step 1

Write $h (x) = \frac{2}{3} x - 4$ as an equation.

$y = \frac{2}{3} x - 4$

Step 2

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

$y = \frac{2 x}{3} - 4$

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.

$y = \frac{2 (0)}{3} - 4$

Step 4.2

Simplify $\frac{2 (0)}{3} - 4$ .

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Step 4.2.1

Multiply $2$ by $0$ .

$y = \frac{0}{3} - 4$

Step 4.2.2

Divide $0$ by $3$ .

$y = 0 - 4$

Step 4.2.3

Subtract $4$ from $0$ .

$y = - 4$

Step 4.3

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

$(0, - 4)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{2 (1)}{3} - 4$

Step 5.2

Simplify $\frac{2 (1)}{3} - 4$ .

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Step 5.2.1

Multiply $2$ by $1$ .

$y = \frac{2}{3} - 4$

Step 5.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{2}{3} - 4 \cdot \frac{3}{3}$

Step 5.2.3

Combine $- 4$ and $\frac{3}{3}$ .

$y = \frac{2}{3} + \frac{- 4 \cdot 3}{3}$

Step 5.2.4

Combine the numerators over the common denominator.

$y = \frac{2 - 4 \cdot 3}{3}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $- 4$ by $3$ .

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

Step 5.2.5.2

Subtract $12$ from $2$ .

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

Step 5.2.6

Move the negative in front of the fraction.

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

Step 5.3

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

$(1, - \frac{10}{3})$

Step 6

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

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Step 6.1

Remove parentheses.

$y = \frac{2 (2)}{3} - 4$

Step 6.2

Simplify $\frac{2 (2)}{3} - 4$ .

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Step 6.2.1

Multiply $2$ by $2$ .

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

Step 6.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6.2.3

Combine $- 4$ and $\frac{3}{3}$ .

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

Step 6.2.4

Combine the numerators over the common denominator.

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

Step 6.2.5

Simplify the numerator.

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Step 6.2.5.1

Multiply $- 4$ by $3$ .

$y = \frac{4 - 12}{3}$

Step 6.2.5.2

Subtract $12$ from $4$ .

$y = \frac{- 8}{3}$

Step 6.2.6

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

Step 6.3

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

$(2, - \frac{8}{3})$

Step 7

These are three possible solutions to the equation.

$(0, - 4), (1, - \frac{10}{3}), (2, - \frac{8}{3})$

Step 8