Pre-Algebra Examples

$y = - \frac{1}{4} x + 5$

Step 1

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

$y = - \frac{1}{4} \cdot - 2 + 5$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = - \frac{1}{4} \cdot - 2 + 5$

Step 2.2

Simplify $- \frac{1}{4} \cdot - 2 + 5$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

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

$y = \frac{- 1}{4} \cdot - 2 + 5$

Step 2.2.1.1.2

Factor $2$ out of $4$ .

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

Step 2.2.1.1.3

Factor $2$ out of $- 2$ .

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

Step 2.2.1.1.4

Cancel the common factor.

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

Step 2.2.1.1.5

Rewrite the expression.

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

Step 2.2.1.2

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

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

Step 2.2.1.3

Multiply $- 1$ by $- 1$ .

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $5$ by $2$ .

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

Step 2.2.5.2

Add $1$ and $10$ .

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

Step 3

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

$y = - \frac{1}{4} \cdot - 1 + 5$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = - \frac{1}{4} \cdot - 1 + 5$

Step 4.2

Simplify $- \frac{1}{4} \cdot - 1 + 5$ .

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Step 4.2.1

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

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{1}{4}) + 5$

Step 4.2.1.2

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

$y = \frac{1}{4} + 5$

Step 4.2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} + 5 \cdot \frac{4}{4}$

Step 4.2.3

Combine $5$ and $\frac{4}{4}$ .

$y = \frac{1}{4} + \frac{5 \cdot 4}{4}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 4}{4}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $5$ by $4$ .

$y = \frac{1 + 20}{4}$

Step 4.2.5.2

Add $1$ and $20$ .

$y = \frac{21}{4}$

Step 5

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

$y = - \frac{1}{4} \cdot 0 + 5$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 0 + 5$

Step 6.2

Simplify $- \frac{1}{4} \cdot 0 + 5$ .

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Step 6.2.1

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

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Step 6.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{4}) + 5$

Step 6.2.1.2

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

$y = 0 + 5$

Step 6.2.2

Add $0$ and $5$ .

$y = 5$

Step 7

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

$y = - \frac{1}{4} \cdot 1 + 5$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 1 + 5$

Step 8.2

Simplify $- \frac{1}{4} \cdot 1 + 5$ .

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Step 8.2.1

Multiply $- 1$ by $1$ .

$y = - \frac{1}{4} + 5$

Step 8.2.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{1}{4} + 5 \cdot \frac{4}{4}$

Step 8.2.3

Combine $5$ and $\frac{4}{4}$ .

$y = - \frac{1}{4} + \frac{5 \cdot 4}{4}$

Step 8.2.4

Combine the numerators over the common denominator.

$y = \frac{- 1 + 5 \cdot 4}{4}$

Step 8.2.5

Simplify the numerator.

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Step 8.2.5.1

Multiply $5$ by $4$ .

$y = \frac{- 1 + 20}{4}$

Step 8.2.5.2

Add $- 1$ and $20$ .

$y = \frac{19}{4}$

Step 9

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

$y = - \frac{1}{4} \cdot 2 + 5$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = - \frac{1}{4} \cdot 2 + 5$

Step 10.2

Simplify $- \frac{1}{4} \cdot 2 + 5$ .

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Step 10.2.1

Simplify each term.

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Step 10.2.1.1

Cancel the common factor of $2$ .

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Step 10.2.1.1.1

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

$y = \frac{- 1}{4} \cdot 2 + 5$

Step 10.2.1.1.2

Factor $2$ out of $4$ .

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

Step 10.2.1.1.3

Cancel the common factor.

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

Step 10.2.1.1.4

Rewrite the expression.

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

Step 10.2.1.2

Move the negative in front of the fraction.

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

Step 10.2.2

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

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

Step 10.2.3

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

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

Step 10.2.4

Combine the numerators over the common denominator.

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

Step 10.2.5

Simplify the numerator.

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Step 10.2.5.1

Multiply $5$ by $2$ .

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

Step 10.2.5.2

Add $- 1$ and $10$ .

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

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{11}{2} \\ - 1 & \frac{21}{4} \\ 0 & 5 \\ 1 & \frac{19}{4} \\ 2 & \frac{9}{2} \end{array}$

Step 12