Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Rewrite.

$y - 5 = 0 + 0 - \frac{1}{2} \cdot (x - 1)$

Step 1.1.2

Simplify by adding zeros.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

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

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

Step 1.1.5

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

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Step 1.1.5.1

Multiply $- 1$ by $- 1$ .

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

Step 1.1.5.2

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

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

Step 1.2

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

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Step 1.2.1

Add $5$ to both sides of the equation.

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

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

Combine the numerators over the common denominator.

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

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $5$ by $2$ .

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

Step 1.2.5.2

Add $1$ and $10$ .

$y = - \frac{x}{2} + \frac{11}{2}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - \frac{0}{2} + \frac{11}{2}$

Step 3.2

Simplify $- \frac{0}{2} + \frac{11}{2}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{0 + 11}{2}$

Step 3.2.2

Add $0$ and $11$ .

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

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, \frac{11}{2})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{1}{2} + \frac{11}{2}$

Step 4.2

Simplify $- \frac{1}{2} + \frac{11}{2}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 1 + 11}{2}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Add $- 1$ and $11$ .

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

Step 4.2.2.2

Divide $10$ by $2$ .

$y = 5$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, 5)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

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

Step 5.2

Simplify $- \frac{2}{2} + \frac{11}{2}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

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

Step 5.2.2

Add $- 2$ and $11$ .

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

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{9}{2})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{11}{2}), (1, 5), (2, \frac{9}{2})$

Step 7