Algebra Examples

$f (x) = \frac{1}{3} x$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $\frac{1}{3}$ by $- 2$ .

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

Step 2.2

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

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Step 2.2.1

Combine $\frac{1}{3}$ and $- 2$ .

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

Step 2.2.2

Move the negative in front of the fraction.

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

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $\frac{1}{3}$ by $- 1$ .

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

Step 4.2

Simplify $\frac{1}{3} \cdot - 1$ .

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Step 4.2.1

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

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

Step 4.2.2

Move the negative in front of the fraction.

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

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Multiply $\frac{1}{3}$ by $0$ .

$y = \frac{1}{3} \cdot 0$

Step 6.2

Remove parentheses.

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

Step 6.3

Multiply $\frac{1}{3}$ by $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $\frac{1}{3}$ by $1$ .

$y = \frac{1}{3} \cdot 1$

Step 8.2

Remove parentheses.

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

Step 8.3

Multiply $\frac{1}{3}$ by $1$ .

$y = \frac{1}{3}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $\frac{1}{3}$ by $2$ .

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

Step 10.2

Remove parentheses.

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

Step 10.3

Combine $\frac{1}{3}$ and $2$ .

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

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{2}{3} \\ - 1 & - \frac{1}{3} \\ 0 & 0 \\ 1 & \frac{1}{3} \\ 2 & \frac{2}{3} \end{array}$

Step 12