Calculus Examples

$y - \frac{π}{4} = 2 (x - \frac{π}{2})$

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 $2 (x - \frac{π}{2})$ .

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Step 2.1.1.1

Apply the distributive property.

$y - \frac{π}{4} = 2 x + 2 (- \frac{π}{2})$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

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

$y - \frac{π}{4} = 2 x + 2 \frac{- π}{2}$

Step 2.1.1.2.2

Cancel the common factor.

$y - \frac{π}{4} = 2 x + 2 \frac{- π}{2}$

Step 2.1.1.2.3

Rewrite the expression.

$y - \frac{π}{4} = 2 x - π$

Step 2.2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.2.1

Add $\frac{π}{4}$ to both sides of the equation.

$y = 2 x - π + \frac{π}{4}$

Step 2.2.2

To write $- π$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = 2 x - π \cdot \frac{4}{4} + \frac{π}{4}$

Step 2.2.3

Combine $- π$ and $\frac{4}{4}$ .

$y = 2 x + \frac{- π \cdot 4}{4} + \frac{π}{4}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = 2 x + \frac{- π \cdot 4 + π}{4}$

Step 2.2.5

Simplify each term.

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Step 2.2.5.1

Simplify the numerator.

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Step 2.2.5.1.1

Multiply $4$ by $- 1$ .

$y = 2 x + \frac{- 4 π + π}{4}$

Step 2.2.5.1.2

Add $- 4 π$ and $π$ .

$y = 2 x + \frac{- 3 π}{4}$

Step 2.2.5.2

Move the negative in front of the fraction.

$y = 2 x - \frac{3 π}{4}$