Pre-Algebra Examples

$y = - \frac{1}{4} x$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Simplify $- \frac{1}{4} \cdot - 2$ .

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 2.2.1.2

Factor $2$ out of $4$ .

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

Step 2.2.1.3

Factor $2$ out of $- 2$ .

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

Step 2.2.1.4

Cancel the common factor.

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

Step 2.2.1.5

Rewrite the expression.

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

Step 2.2.2

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

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

Step 2.2.3

Multiply $- 1$ by $- 1$ .

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

Step 3

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

$y = - \frac{1}{4} \cdot - 1$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = - \frac{1}{4} \cdot - 1$

Step 4.2

Multiply $- \frac{1}{4} \cdot - 1$ .

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Step 4.2.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{1}{4})$

Step 4.2.2

Multiply $\frac{1}{4}$ by $1$ .

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

Step 5

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

$y = - \frac{1}{4} \cdot 0$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 0$

Step 6.2

Multiply $- \frac{1}{4} \cdot 0$ .

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Step 6.2.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{4})$

Step 6.2.2

Multiply $0$ by $\frac{1}{4}$ .

$y = 0$

Step 7

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

$y = - \frac{1}{4} \cdot 1$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 1$

Step 8.2

Multiply $- 1$ by $1$ .

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Simplify $- \frac{1}{4} \cdot 2$ .

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Step 10.2.1

Cancel the common factor of $2$ .

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Step 10.2.1.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 10.2.1.2

Factor $2$ out of $4$ .

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

Step 10.2.1.3

Cancel the common factor.

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

Step 10.2.1.4

Rewrite the expression.

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

Step 10.2.2

Move the negative in front of the fraction.

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

Step 11

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

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

Step 12