Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $\frac{2}{3} (x - 1)$ .

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Step 1.1.1

Rewrite.

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

Step 1.1.2

Simplify by adding zeros.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.1.4

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

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

Step 1.1.5

Multiply $\frac{2}{3} \cdot - 1$ .

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Step 1.1.5.1

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

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

Step 1.1.5.2

Multiply $2$ by $- 1$ .

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

Step 1.1.6

Move the negative in front of the fraction.

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

Step 1.2

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

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Step 1.2.1

Add $3$ to both sides of the equation.

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

Step 1.2.2

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

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

Step 1.2.3

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

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

Step 1.2.4

Combine the numerators over the common denominator.

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

Step 1.2.5

Simplify the numerator.

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Step 1.2.5.1

Multiply $3$ by $3$ .

$y = \frac{2 x}{3} + \frac{- 2 + 9}{3}$

Step 1.2.5.2

Add $- 2$ and $9$ .

$y = \frac{2 x}{3} + \frac{7}{3}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear