Algebra Examples

$y = \frac{1}{2} x - 5$

Step 1

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

$y = \frac{1}{2} \cdot (- 2) - 5$

Step 2

Solve the equation for $y$ .

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

$y = \frac{1}{2} \cdot - 2 - 5$

Simplify $\frac{1}{2} \cdot - 2 - 5$ .

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Cancel the common factor of $2$ .

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Factor $2$ out of $- 2$ .

$y = \frac{1}{2} \cdot (2 (- 1)) - 5$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot - 1) - 5$

Rewrite the expression.

$y = - 1 - 5$

Subtract $5$ from $- 1$ .

$y = - 6$

Step 3

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

$y = \frac{1}{2} \cdot (- 1) - 5$

Step 4

Solve the equation for $y$ .

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

$y = \frac{1}{2} \cdot - 1 - 5$

Simplify $\frac{1}{2} \cdot - 1 - 5$ .

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Simplify each term.

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

$y = \frac{- 1}{2} - 5$

Move the negative in front of the fraction.

$y = - \frac{1}{2} - 5$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{1}{2} - 5 \cdot \frac{2}{2}$

Combine $- 5$ and $\frac{2}{2}$ .

$y = - \frac{1}{2} + \frac{- 5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 1 - 5 \cdot 2}{2}$

Simplify the numerator.

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Multiply $- 5$ by $2$ .

$y = \frac{- 1 - 10}{2}$

Subtract $10$ from $- 1$ .

$y = \frac{- 11}{2}$

Move the negative in front of the fraction.

$y = - \frac{11}{2}$

Step 5

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

$y = \frac{1}{2} \cdot (0) - 5$

Step 6

Solve the equation for $y$ .

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

$y = \frac{1}{2} \cdot 0 - 5$

Remove parentheses.

$y = \frac{1}{2} \cdot (0) - 5$

Simplify $\frac{1}{2} \cdot (0) - 5$ .

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

$y = 0 - 5$

Subtract $5$ from $0$ .

$y = - 5$

Step 7

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

$y = \frac{1}{2} \cdot (1) - 5$

Step 8

Solve the equation for $y$ .

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

$y = \frac{1}{2} \cdot 1 - 5$

Remove parentheses.

$y = \frac{1}{2} \cdot (1) - 5$

Simplify $\frac{1}{2} \cdot (1) - 5$ .

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

$y = \frac{1}{2} - 5$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{1}{2} - 5 \cdot \frac{2}{2}$

Combine $- 5$ and $\frac{2}{2}$ .

$y = \frac{1}{2} + \frac{- 5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{1 - 5 \cdot 2}{2}$

Simplify the numerator.

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Multiply $- 5$ by $2$ .

$y = \frac{1 - 10}{2}$

Subtract $10$ from $1$ .

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

Move the negative in front of the fraction.

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

Step 9

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

$y = \frac{1}{2} \cdot (2) - 5$

Step 10

Solve the equation for $y$ .

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

$y = \frac{1}{2} \cdot 2 - 5$

Remove parentheses.

$y = \frac{1}{2} \cdot (2) - 5$

Simplify $\frac{1}{2} \cdot (2) - 5$ .

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Cancel the common factor of $2$ .

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Cancel the common factor.

$y = \frac{1}{2} \cdot 2 - 5$

Rewrite the expression.

$y = 1 - 5$

Subtract $5$ from $1$ .

$y = - 4$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - \frac{11}{2} \\ 0 & - 5 \\ 1 & - \frac{9}{2} \\ 2 & - 4 \end{array}$

Step 12