Calculus Examples

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

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 $\frac{2}{3} (x - \frac{π}{6})$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Factor $2$ out of $6$ .

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

Step 2.1.1.3.3

Cancel the common factor.

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

Step 2.1.1.3.4

Rewrite the expression.

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

Step 2.1.1.4

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

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

Step 2.1.1.5

Simplify the expression.

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Step 2.1.1.5.1

Multiply $3$ by $3$ .

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

Step 2.1.1.5.2

Move the negative in front of the fraction.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.2.1

Multiply $\frac{\sqrt{3}}{3}$ by $\frac{3}{3}$ .

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

Step 2.3.2.2

Multiply $3$ by $3$ .

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

Step 2.3.3

Combine the numerators over the common denominator.

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

Step 2.3.4

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

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

Step 2.3.5

Factor $- 1$ out of $- π$ .

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

Step 2.3.6

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

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

Step 2.3.7

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

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

Step 2.3.8

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

$y = \frac{2 x}{3} + \frac{- 1 (π - 3 \sqrt{3})}{9}$

Step 2.3.9

Move the negative in front of the fraction.

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

Step 2.3.10

Reorder terms.

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