Algebra Examples

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

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

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Step 2.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} \cdot ((- 2) + 2)$

Step 2.1.2

Simplify by adding zeros.

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

Step 2.1.3

Add $- 2$ and $2$ .

$y - 3 = \frac{1}{2} \cdot 0$

Step 2.1.4

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

$y - 3 = 0$

Step 2.2

Add $3$ to both sides of the equation.

$y = 3$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

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

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Step 4.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} \cdot ((- 1) + 2)$

Step 4.1.2

Simplify by adding zeros.

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

Step 4.1.3

Add $- 1$ and $2$ .

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

Step 4.1.4

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

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

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 $3$ to both sides of the equation.

$y = \frac{1}{2} + 3$

Step 4.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.3

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

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $3$ by $2$ .

$y = \frac{1 + 6}{2}$

Step 4.2.5.2

Add $1$ and $6$ .

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

Step 5

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

$y - 3 = \frac{1}{2} \cdot ((0) + 2)$

Step 6

Solve the equation for $y$ .

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Step 6.1

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

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Step 6.1.1

Add $0$ and $2$ .

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

Step 6.1.2

Cancel the common factor of $2$ .

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Step 6.1.2.1

Cancel the common factor.

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

Step 6.1.2.2

Rewrite the expression.

$y - 3 = 1$

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 $3$ to both sides of the equation.

$y = 1 + 3$

Step 6.2.2

Add $1$ and $3$ .

$y = 4$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

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

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Step 8.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} \cdot ((1) + 2)$

Step 8.1.2

Add $1$ and $2$ .

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

Step 8.1.3

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

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

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 $3$ to both sides of the equation.

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

Step 8.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 8.2.3

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

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

Step 8.2.4

Combine the numerators over the common denominator.

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

Step 8.2.5

Simplify the numerator.

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Step 8.2.5.1

Multiply $3$ by $2$ .

$y = \frac{3 + 6}{2}$

Step 8.2.5.2

Add $3$ and $6$ .

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

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

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Step 10.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{1}{2} \cdot ((2) + 2)$

Step 10.1.2

Add $2$ and $2$ .

$y - 3 = \frac{1}{2} \cdot 4$

Step 10.1.3

Cancel the common factor of $2$ .

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Step 10.1.3.1

Factor $2$ out of $4$ .

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

Step 10.1.3.2

Cancel the common factor.

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

Step 10.1.3.3

Rewrite the expression.

$y - 3 = 2$

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 $3$ to both sides of the equation.

$y = 2 + 3$

Step 10.2.2

Add $2$ and $3$ .

$y = 5$

Step 11

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

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

Step 12