Find Three Ordered Pair Solutions k(x)=2/9|x|

$k (x) = \frac{2}{9} | x |$

Step 1

Write $k (x) = \frac{2}{9} | x |$ as an equation.

$y = \frac{2}{9} | x |$

Step 2

Combine $\frac{2}{9}$ and $| x |$ .

$y = \frac{2 | x |}{9}$

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.

Simplify $\frac{2 | 0 |}{9}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = \frac{2 \cdot 0}{9}$

Multiply $2$ by $0$ .

$y = \frac{0}{9}$

Divide $0$ by $9$ .

$y = 0$

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.

Simplify $\frac{2 | 1 |}{9}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$y = \frac{2 \cdot 1}{9}$

Multiply $2$ by $1$ .

$y = \frac{2}{9}$

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

$(1, \frac{2}{9})$

Step 6

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

Simplify $\frac{2 | 2 |}{9}$ .

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$y = \frac{2 \cdot 2}{9}$

Multiply $2$ by $2$ .

$y = \frac{4}{9}$

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

$(2, \frac{4}{9})$

Step 7

These are three possible solutions to the equation.

$(0, 0), (1, \frac{2}{9}), (2, \frac{4}{9})$

Step 8