Algebra Examples

$(y - 4) = - \frac{1}{4} (x + 3)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $- \frac{1}{4} \cdot (x + 3)$ .

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Step 1.1.1

Rewrite.

$y - 4 = 0 + 0 - \frac{1}{4} \cdot (x + 3)$

Step 1.1.2

Simplify by adding zeros.

$y - 4 = - \frac{1}{4} \cdot (x + 3)$

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

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

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

Step 1.1.5

Multiply $- \frac{1}{4} \cdot 3$ .

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Step 1.1.5.1

Multiply $3$ by $- 1$ .

$y - 4 = - \frac{x}{4} - 3 (\frac{1}{4})$

Step 1.1.5.2

Combine $- 3$ and $\frac{1}{4}$ .

$y - 4 = - \frac{x}{4} + \frac{- 3}{4}$

Step 1.1.6

Move the negative in front of the fraction.

$y - 4 = - \frac{x}{4} - \frac{3}{4}$

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 $4$ to both sides of the equation.

$y = - \frac{x}{4} - \frac{3}{4} + 4$

Step 1.2.2

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

$y = - \frac{x}{4} - \frac{3}{4} + 4 \cdot \frac{4}{4}$

Step 1.2.3

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

$y = - \frac{x}{4} - \frac{3}{4} + \frac{4 \cdot 4}{4}$

Step 1.2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{4} + \frac{- 3 + 4 \cdot 4}{4}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $4$ by $4$ .

$y = - \frac{x}{4} + \frac{- 3 + 16}{4}$

Step 1.2.5.2

Add $- 3$ and $16$ .

$y = - \frac{x}{4} + \frac{13}{4}$

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.

$y = - \frac{0}{4} + \frac{13}{4}$

Step 3.2

Simplify $- \frac{0}{4} + \frac{13}{4}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{0 + 13}{4}$

Step 3.2.2

Add $0$ and $13$ .

$y = \frac{13}{4}$

Step 3.3

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

$(0, \frac{13}{4})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{1}{4} + \frac{13}{4}$

Step 4.2

Simplify $- \frac{1}{4} + \frac{13}{4}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 1 + 13}{4}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Add $- 1$ and $13$ .

$y = \frac{12}{4}$

Step 4.2.2.2

Divide $12$ by $4$ .

$y = 3$

Step 4.3

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

$(1, 3)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{2}{4} + \frac{13}{4}$

Step 5.2

Simplify $- \frac{2}{4} + \frac{13}{4}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 2 + 13}{4}$

Step 5.2.2

Add $- 2$ and $13$ .

$y = \frac{11}{4}$

Step 5.3

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

$(2, \frac{11}{4})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{13}{4}), (1, 3), (2, \frac{11}{4})$

Step 7