Calculus Examples

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

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 left side.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Divide $3$ by $3$ .

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

Step 2.1.1.2

Any root of $1$ is $1$ .

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

Step 2.1.1.3

Multiply $- 2$ by $1$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Apply the distributive property.

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

Step 2.2.1.2

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

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

Step 2.2.1.3

Cancel the common factor of $2$ .

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Step 2.2.1.3.1

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

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

Step 2.2.1.3.2

Factor $2$ out of $6$ .

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

Step 2.2.1.3.3

Cancel the common factor.

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

Step 2.2.1.3.4

Rewrite the expression.

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

Step 2.2.1.4

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

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

Step 2.2.1.5

Simplify the expression.

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Step 2.2.1.5.1

Multiply $3$ by $3$ .

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

Step 2.2.1.5.2

Move the negative in front of the fraction.

$y - 2 = \frac{2 x}{3} - \frac{π}{9}$

Step 2.3

Add $2$ to both sides of the equation.

$y = \frac{2 x}{3} - \frac{π}{9} + 2$

Step 2.4

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

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Step 2.4.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Step 2.4.2

Combine $2$ and $\frac{9}{9}$ .

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

Step 2.4.3

Combine the numerators over the common denominator.

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

Step 2.4.4

Multiply $2$ by $9$ .

$y = \frac{2 x}{3} + \frac{- π + 18}{9}$

Step 2.4.5

Factor $- 1$ out of $- π$ .

$y = \frac{2 x}{3} + \frac{- (π) + 18}{9}$

Step 2.4.6

Rewrite $18$ as $- 1 (- 18)$ .

$y = \frac{2 x}{3} + \frac{- (π) - 1 (- 18)}{9}$

Step 2.4.7

Factor $- 1$ out of $- (π) - 1 (- 18)$ .

$y = \frac{2 x}{3} + \frac{- (π - 18)}{9}$

Step 2.4.8

Rewrite $- (π - 18)$ as $- 1 (π - 18)$ .

$y = \frac{2 x}{3} + \frac{- 1 (π - 18)}{9}$

Step 2.4.9

Move the negative in front of the fraction.

$y = \frac{2 x}{3} - \frac{π - 18}{9}$

Step 2.4.10

Reorder terms.

$y = \frac{2}{3} x - \frac{π - 18}{9}$