Calculus Examples

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

Step 1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the right side.

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Step 2.1.1

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

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Multiply $2 \sqrt{3} (- \frac{π}{3})$ .

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Step 2.1.1.2.1

Multiply $- 1$ by $2$ .

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

Step 2.1.1.2.2

Combine $\frac{π}{3}$ and $- 2$ .

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

Step 2.1.1.2.3

Combine $\frac{π \cdot - 2}{3}$ and $\sqrt{3}$ .

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

Step 2.1.1.3

Simplify each term.

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Step 2.1.1.3.1

Move $- 2$ to the left of $π$ .

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

Step 2.1.1.3.2

Move the negative in front of the fraction.

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

Step 2.2

Add $2$ to both sides of the equation.

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

Step 2.3

Write in $y = m x + b$ form.

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Step 2.3.1

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

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

Step 2.3.2

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

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

Step 2.3.3

Combine the numerators over the common denominator.

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

Step 2.3.4

Multiply $2$ by $3$ .

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

Step 2.3.5

Factor $- 1$ out of $- 2 π \sqrt{3}$ .

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

Step 2.3.6

Rewrite $6$ as $- 1 (- 6)$ .

$y = 2 \sqrt{3} x + \frac{- (2 π \sqrt{3}) - 1 (- 6)}{3}$

Step 2.3.7

Factor $- 1$ out of $- (2 π \sqrt{3}) - 1 (- 6)$ .

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

Step 2.3.8

Rewrite $- (2 π \sqrt{3} - 6)$ as $- 1 (2 π \sqrt{3} - 6)$ .

$y = 2 \sqrt{3} x + \frac{- 1 (2 π \sqrt{3} - 6)}{3}$

Step 2.3.9

Move the negative in front of the fraction.

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