Calculus Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Combine $\frac{1}{3}$ and $x$ .

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

Step 1.5

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

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

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

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

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $3$ .

$y = \frac{x}{3} + \frac{2 + 6}{3}$

Step 2.5.2

Add $2$ and $6$ .

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