Calculus Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify terms.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 1.2.2.2

Factor $2$ out of $2 \sqrt{3}$ .

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

Step 1.2.2.3

Cancel the common factor.

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

Step 1.2.2.4

Rewrite the expression.

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

Step 1.3

Simplify each term.

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Step 1.3.1

Move $- 1$ to the left of $\sqrt{3}$ .

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

Step 1.3.2

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

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

Step 2

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

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