Algebra Examples

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

Step 1

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

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

Step 2

Simplify $- \frac{- 2}{4} + 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $- 2$ and $4$ .

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Step 2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 2.1.1.2

Cancel the common factors.

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Step 2.1.1.2.1

Factor $2$ out of $4$ .

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

Step 2.1.1.2.2

Cancel the common factor.

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

Step 2.1.1.2.3

Rewrite the expression.

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

Step 2.1.2

Move the negative in front of the fraction.

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

Step 2.1.3

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

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.3.2

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

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

Step 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 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

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

Step 2.5.2

Add $1$ and $4$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Simplify each term.

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Step 4.1.1

Move the negative in front of the fraction.

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

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.1.2.2

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

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

Step 4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4.3

Combine $2$ and $\frac{4}{4}$ .

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $4$ .

$y = \frac{1 + 8}{4}$

Step 4.5.2

Add $1$ and $8$ .

$y = \frac{9}{4}$

Step 5

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

$y = - \frac{0}{4} + 2$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - \frac{0}{4} + 2$

Step 6.2

Simplify $- \frac{0}{4} + 2$ .

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Step 6.2.1

Simplify each term.

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Step 6.2.1.1

Divide $0$ by $4$ .

$y = - 0 + 2$

Step 6.2.1.2

Multiply $- 1$ by $0$ .

$y = 0 + 2$

Step 6.2.2

Add $0$ and $2$ .

$y = 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

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

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Step 8.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 8.2.2

Combine $2$ and $\frac{4}{4}$ .

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

Step 8.2.3

Combine the numerators over the common denominator.

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

Step 8.2.4

Simplify the numerator.

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Step 8.2.4.1

Multiply $2$ by $4$ .

$y = \frac{- 1 + 8}{4}$

Step 8.2.4.2

Add $- 1$ and $8$ .

$y = \frac{7}{4}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Simplify $- \frac{2}{4} + 2$ .

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Step 10.2.1

Cancel the common factor of $2$ and $4$ .

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Step 10.2.1.1

Factor $2$ out of $2$ .

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

Step 10.2.1.2

Cancel the common factors.

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Step 10.2.1.2.1

Factor $2$ out of $4$ .

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

Step 10.2.1.2.2

Cancel the common factor.

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

Step 10.2.1.2.3

Rewrite the expression.

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

Step 10.2.2

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 10.2.3

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

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

Step 10.2.4

Combine the numerators over the common denominator.

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

Step 10.2.5

Simplify the numerator.

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Step 10.2.5.1

Multiply $2$ by $2$ .

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

Step 10.2.5.2

Add $- 1$ and $4$ .

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

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{5}{2} \\ - 1 & \frac{9}{4} \\ 0 & 2 \\ 1 & \frac{7}{4} \\ 2 & \frac{3}{2} \end{array}$

Step 12