Algebra Examples

$f (x) = \frac{1}{2} x + 2$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $- 2$ .

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

Step 2.2.1.2

Cancel the common factor.

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

Step 2.2.1.3

Rewrite the expression.

$y = - 1 + 2$

Step 2.2.2

Add $- 1$ and $2$ .

$y = 1$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

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

$y = \frac{- 1}{2} + 2$

Step 4.2.1.2

Move the negative in front of the fraction.

$y = - \frac{1}{2} + 2$

Step 4.2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.3

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

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $2$ by $2$ .

$y = \frac{- 1 + 4}{2}$

Step 4.2.5.2

Add $- 1$ and $4$ .

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

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

$y = \frac{1}{2} \cdot 0 + 2$

Step 6.2

Remove parentheses.

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

Step 6.3

Simplify $\frac{1}{2} \cdot (0) + 2$ .

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Step 6.3.1

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

$y = 0 + 2$

Step 6.3.2

Add $0$ and $2$ .

$y = 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

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

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

Step 8.2

Remove parentheses.

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

Step 8.3

Simplify $\frac{1}{2} \cdot (1) + 2$ .

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Step 8.3.1

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

$y = \frac{1}{2} + 2$

Step 8.3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 8.3.3

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

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

Step 8.3.4

Combine the numerators over the common denominator.

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

Step 8.3.5

Simplify the numerator.

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Step 8.3.5.1

Multiply $2$ by $2$ .

$y = \frac{1 + 4}{2}$

Step 8.3.5.2

Add $1$ and $4$ .

$y = \frac{5}{2}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

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

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

Step 10.2

Remove parentheses.

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

Step 10.3

Simplify $\frac{1}{2} \cdot (2) + 2$ .

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Step 10.3.1

Cancel the common factor of $2$ .

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Step 10.3.1.1

Cancel the common factor.

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

Step 10.3.1.2

Rewrite the expression.

$y = 1 + 2$

Step 10.3.2

Add $1$ and $2$ .

$y = 3$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 1 \\ - 1 & \frac{3}{2} \\ 0 & 2 \\ 1 & \frac{5}{2} \\ 2 & 3 \end{array}$

Step 12