Calculus Examples

$y - \frac{2 \sqrt{3}}{3} = \frac{2}{3} \cdot (x - \frac{π}{6})$

Step 1

Simplify $\frac{2}{3} \cdot (x - \frac{π}{6})$ .

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Step 1.1

Rewrite.

$y - \frac{2 \sqrt{3}}{3} = 0 + 0 + \frac{2}{3} \cdot (x - \frac{π}{6})$

Step 1.2

Simplify by adding zeros.

$y - \frac{2 \sqrt{3}}{3} = \frac{2}{3} \cdot (x - \frac{π}{6})$

Step 1.3

Apply the distributive property.

$y - \frac{2 \sqrt{3}}{3} = \frac{2}{3} x + \frac{2}{3} (- \frac{π}{6})$

Step 1.4

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

$y - \frac{2 \sqrt{3}}{3} = \frac{2 x}{3} + \frac{2}{3} (- \frac{π}{6})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Move the leading negative in $- \frac{π}{6}$ into the numerator.

$y - \frac{2 \sqrt{3}}{3} = \frac{2 x}{3} + \frac{2}{3} \cdot \frac{- π}{6}$

Step 1.5.2

Factor $2$ out of $6$ .

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

Step 1.5.3

Cancel the common factor.

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

Step 1.5.4

Rewrite the expression.

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

Step 1.6

Multiply $\frac{1}{3}$ by $\frac{- π}{3}$ .

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

Step 1.7

Simplify the expression.

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Step 1.7.1

Multiply $3$ by $3$ .

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

Step 1.7.2

Move the negative in front of the fraction.

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

Step 2

Add $\frac{2 \sqrt{3}}{3}$ to both sides of the equation.

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