Algebra Examples

$y - 2 = \frac{1}{4} (x + 8)$

Step 1

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

$y - 2 = \frac{1}{4} \cdot ((- 2) + 8)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $\frac{1}{4} \cdot ((- 2) + 8)$ .

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Step 2.1.1

Rewrite.

$y - 2 = 0 + 0 + \frac{1}{4} \cdot ((- 2) + 8)$

Step 2.1.2

Add $- 2$ and $8$ .

$y - 2 = \frac{1}{4} \cdot 6$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Factor $2$ out of $4$ .

$y - 2 = \frac{1}{2 (2)} \cdot 6$

Step 2.1.3.2

Factor $2$ out of $6$ .

$y - 2 = \frac{1}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 2.1.3.3

Cancel the common factor.

$y - 2 = \frac{1}{2 \cdot 2} \cdot (2 \cdot 3)$

Step 2.1.3.4

Rewrite the expression.

$y - 2 = \frac{1}{2} \cdot 3$

Step 2.1.4

Combine $\frac{1}{2}$ and $3$ .

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

Step 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Add $2$ to both sides of the equation.

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $2$ by $2$ .

$y = \frac{3 + 4}{2}$

Step 2.2.5.2

Add $3$ and $4$ .

$y = \frac{7}{2}$

Step 3

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

$y - 2 = \frac{1}{4} \cdot ((- 1) + 8)$

Step 4

Solve the equation for $y$ .

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Step 4.1

Simplify $\frac{1}{4} \cdot ((- 1) + 8)$ .

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Step 4.1.1

Rewrite.

$y - 2 = 0 + 0 + \frac{1}{4} \cdot ((- 1) + 8)$

Step 4.1.2

Add $- 1$ and $8$ .

$y - 2 = \frac{1}{4} \cdot 7$

Step 4.1.3

Combine $\frac{1}{4}$ and $7$ .

$y - 2 = \frac{7}{4}$

Step 4.2

Move all terms not containing $y$ to the right side of the equation.

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Step 4.2.1

Add $2$ to both sides of the equation.

$y = \frac{7}{4} + 2$

Step 4.2.2

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

$y = \frac{7}{4} + 2 \cdot \frac{4}{4}$

Step 4.2.3

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

$y = \frac{7}{4} + \frac{2 \cdot 4}{4}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{7 + 2 \cdot 4}{4}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $2$ by $4$ .

$y = \frac{7 + 8}{4}$

Step 4.2.5.2

Add $7$ and $8$ .

$y = \frac{15}{4}$

Step 5

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

$y - 2 = \frac{1}{4} \cdot ((0) + 8)$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $\frac{1}{4} \cdot ((0) + 8)$ .

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Step 6.1.1

Add $0$ and $8$ .

$y - 2 = \frac{1}{4} \cdot 8$

Step 6.1.2

Cancel the common factor of $4$ .

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Step 6.1.2.1

Factor $4$ out of $8$ .

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

Step 6.1.2.2

Cancel the common factor.

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

Step 6.1.2.3

Rewrite the expression.

$y - 2 = 2$

Step 6.2

Move all terms not containing $y$ to the right side of the equation.

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Step 6.2.1

Add $2$ to both sides of the equation.

$y = 2 + 2$

Step 6.2.2

Add $2$ and $2$ .

$y = 4$

Step 7

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

$y - 2 = \frac{1}{4} \cdot ((1) + 8)$

Step 8

Solve the equation for $y$ .

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Step 8.1

Simplify $\frac{1}{4} \cdot ((1) + 8)$ .

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Step 8.1.1

Rewrite.

$y - 2 = 0 + 0 + \frac{1}{4} \cdot ((1) + 8)$

Step 8.1.2

Add $1$ and $8$ .

$y - 2 = \frac{1}{4} \cdot 9$

Step 8.1.3

Combine $\frac{1}{4}$ and $9$ .

$y - 2 = \frac{9}{4}$

Step 8.2

Move all terms not containing $y$ to the right side of the equation.

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Step 8.2.1

Add $2$ to both sides of the equation.

$y = \frac{9}{4} + 2$

Step 8.2.2

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

$y = \frac{9}{4} + 2 \cdot \frac{4}{4}$

Step 8.2.3

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

$y = \frac{9}{4} + \frac{2 \cdot 4}{4}$

Step 8.2.4

Combine the numerators over the common denominator.

$y = \frac{9 + 2 \cdot 4}{4}$

Step 8.2.5

Simplify the numerator.

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Step 8.2.5.1

Multiply $2$ by $4$ .

$y = \frac{9 + 8}{4}$

Step 8.2.5.2

Add $9$ and $8$ .

$y = \frac{17}{4}$

Step 9

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

$y - 2 = \frac{1}{4} \cdot ((2) + 8)$

Step 10

Solve the equation for $y$ .

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Step 10.1

Simplify $\frac{1}{4} \cdot ((2) + 8)$ .

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Step 10.1.1

Rewrite.

$y - 2 = 0 + 0 + \frac{1}{4} \cdot ((2) + 8)$

Step 10.1.2

Add $2$ and $8$ .

$y - 2 = \frac{1}{4} \cdot 10$

Step 10.1.3

Cancel the common factor of $2$ .

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Step 10.1.3.1

Factor $2$ out of $4$ .

$y - 2 = \frac{1}{2 (2)} \cdot 10$

Step 10.1.3.2

Factor $2$ out of $10$ .

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

Step 10.1.3.3

Cancel the common factor.

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

Step 10.1.3.4

Rewrite the expression.

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

Step 10.1.4

Combine $\frac{1}{2}$ and $5$ .

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

Step 10.2

Move all terms not containing $y$ to the right side of the equation.

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Step 10.2.1

Add $2$ to both sides of the equation.

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

Step 10.2.2

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

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

Step 10.2.3

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

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

Step 10.2.4

Combine the numerators over the common denominator.

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

Step 10.2.5

Simplify the numerator.

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Step 10.2.5.1

Multiply $2$ by $2$ .

$y = \frac{5 + 4}{2}$

Step 10.2.5.2

Add $5$ and $4$ .

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

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{7}{2} \\ - 1 & \frac{15}{4} \\ 0 & 4 \\ 1 & \frac{17}{4} \\ 2 & \frac{9}{2} \end{array}$

Step 12