Algebra Examples

$y + 4 = - \frac{4}{3} (x + 2)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $- \frac{4}{3} \cdot (x + 2)$ .

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Step 1.1.1

Rewrite.

$y + 4 = 0 + 0 - \frac{4}{3} \cdot (x + 2)$

Step 1.1.2

Simplify by adding zeros.

$y + 4 = - \frac{4}{3} \cdot (x + 2)$

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

Combine $x$ and $\frac{4}{3}$ .

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

Step 1.1.5

Multiply $- \frac{4}{3} \cdot 2$ .

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Step 1.1.5.1

Multiply $2$ by $- 1$ .

$y + 4 = - \frac{x \cdot 4}{3} - 2 (\frac{4}{3})$

Step 1.1.5.2

Combine $- 2$ and $\frac{4}{3}$ .

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

Step 1.1.5.3

Multiply $- 2$ by $4$ .

$y + 4 = - \frac{x \cdot 4}{3} + \frac{- 8}{3}$

Step 1.1.6

Simplify each term.

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Step 1.1.6.1

Move $4$ to the left of $x$ .

$y + 4 = - \frac{4 \cdot x}{3} + \frac{- 8}{3}$

Step 1.1.6.2

Move the negative in front of the fraction.

$y + 4 = - \frac{4 x}{3} - \frac{8}{3}$

Step 1.2

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

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Step 1.2.1

Subtract $4$ from both sides of the equation.

$y = - \frac{4 x}{3} - \frac{8}{3} - 4$

Step 1.2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{4 x}{3} - \frac{8}{3} - 4 \cdot \frac{3}{3}$

Step 1.2.3

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

$y = - \frac{4 x}{3} - \frac{8}{3} + \frac{- 4 \cdot 3}{3}$

Step 1.2.4

Combine the numerators over the common denominator.

$y = - \frac{4 x}{3} + \frac{- 8 - 4 \cdot 3}{3}$

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $- 4$ by $3$ .

$y = - \frac{4 x}{3} + \frac{- 8 - 12}{3}$

Step 1.2.5.2

Subtract $12$ from $- 8$ .

$y = - \frac{4 x}{3} + \frac{- 20}{3}$

Step 1.2.6

Move the negative in front of the fraction.

$y = - \frac{4 x}{3} - \frac{20}{3}$

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.

$y = - \frac{4 (0)}{3} - \frac{20}{3}$

Step 3.2

Simplify $- \frac{4 (0)}{3} - \frac{20}{3}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{- 4 \cdot 0 - 20}{3}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Multiply $- 4$ by $0$ .

$y = \frac{0 - 20}{3}$

Step 3.2.2.2

Subtract $20$ from $0$ .

$y = \frac{- 20}{3}$

Step 3.2.2.3

Move the negative in front of the fraction.

$y = - \frac{20}{3}$

Step 3.3

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

$(0, - \frac{20}{3})$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - \frac{4 (1)}{3} - \frac{20}{3}$

Step 4.2

Simplify $- \frac{4 (1)}{3} - \frac{20}{3}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{- 4 \cdot 1 - 20}{3}$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply $- 4$ by $1$ .

$y = \frac{- 4 - 20}{3}$

Step 4.2.2.2

Subtract $20$ from $- 4$ .

$y = \frac{- 24}{3}$

Step 4.2.2.3

Divide $- 24$ by $3$ .

$y = - 8$

Step 4.3

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

$(1, - 8)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - \frac{4 (2)}{3} - \frac{20}{3}$

Step 5.2

Simplify $- \frac{4 (2)}{3} - \frac{20}{3}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{- 4 \cdot 2 - 20}{3}$

Step 5.2.2

Simplify the expression.

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Step 5.2.2.1

Multiply $- 4$ by $2$ .

$y = \frac{- 8 - 20}{3}$

Step 5.2.2.2

Subtract $20$ from $- 8$ .

$y = \frac{- 28}{3}$

Step 5.2.2.3

Move the negative in front of the fraction.

$y = - \frac{28}{3}$

Step 5.3

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

$(2, - \frac{28}{3})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{20}{3}), (1, - 8), (2, - \frac{28}{3})$

Step 7