Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Rewrite.

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

Step 1.1.2

Simplify terms.

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Step 1.1.2.1

Apply the distributive property.

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Cancel the common factor of $3$ .

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Step 1.1.2.3.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Step 1.1.2.3.2

Cancel the common factor.

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

Step 1.1.2.3.3

Rewrite the expression.

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

Step 1.1.3

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

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

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.

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

Step 1.2.2

Combine the opposite terms in $- \frac{4 x}{3} - 4 + 4$ .

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Step 1.2.2.1

Add $- 4$ and $4$ .

$y = - \frac{4 x}{3} + 0$

Step 1.2.2.2

Add $- \frac{4 x}{3}$ and $0$ .

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

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.

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor of $0$ and $3$ .

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Step 3.2.1.1

Factor $3$ out of $4 (0)$ .

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

Step 3.2.1.2

Cancel the common factors.

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Step 3.2.1.2.1

Factor $3$ out of $3$ .

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

Step 3.2.1.2.2

Cancel the common factor.

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

Step 3.2.1.2.3

Rewrite the expression.

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

Step 3.2.1.2.4

Divide $4 \cdot (0)$ by $1$ .

$y = - (4 \cdot (0))$

Step 3.2.2

Multiply $- (4 \cdot (0))$ .

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Step 3.2.2.1

Multiply $4$ by $0$ .

$y = - 0$

Step 3.2.2.2

Multiply $- 1$ by $0$ .

$y = 0$

Step 3.3

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

$(0, 0)$

Step 4

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

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Step 4.1

Remove parentheses.

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

Step 4.2

Multiply $4$ by $1$ .

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

Step 4.3

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

$(1, - \frac{4}{3})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Multiply $4$ by $2$ .

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

Step 5.3

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

$(2, - \frac{8}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, - \frac{4}{3}), (2, - \frac{8}{3})$

Step 7