Calculus Examples

$y - \frac{π}{4} = \frac{1}{6} (x - 3)$

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 $\frac{1}{6} (x - 3)$ .

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Step 2.1.1.1

Apply the distributive property.

$y - \frac{π}{4} = \frac{1}{6} x + \frac{1}{6} \cdot - 3$

Step 2.1.1.2

Combine $\frac{1}{6}$ and $x$ .

$y - \frac{π}{4} = \frac{x}{6} + \frac{1}{6} \cdot - 3$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $6$ .

$y - \frac{π}{4} = \frac{x}{6} + \frac{1}{3 (2)} \cdot - 3$

Step 2.1.1.3.2

Factor $3$ out of $- 3$ .

$y - \frac{π}{4} = \frac{x}{6} + \frac{1}{3 \cdot 2} \cdot (3 \cdot - 1)$

Step 2.1.1.3.3

Cancel the common factor.

$y - \frac{π}{4} = \frac{x}{6} + \frac{1}{3 \cdot 2} \cdot (3 \cdot - 1)$

Step 2.1.1.3.4

Rewrite the expression.

$y - \frac{π}{4} = \frac{x}{6} + \frac{1}{2} \cdot - 1$

Step 2.1.1.4

Combine $\frac{1}{2}$ and $- 1$ .

$y - \frac{π}{4} = \frac{x}{6} + \frac{- 1}{2}$

Step 2.1.1.5

Move the negative in front of the fraction.

$y - \frac{π}{4} = \frac{x}{6} - \frac{1}{2}$

Step 2.2

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

$y = \frac{x}{6} - \frac{1}{2} + \frac{π}{4}$

Step 2.3

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

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Step 2.3.1

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{x}{6} - \frac{1}{2} \cdot \frac{2}{2} + \frac{π}{4}$

Step 2.3.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.2.1

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$y = \frac{x}{6} - \frac{2}{2 \cdot 2} + \frac{π}{4}$

Step 2.3.2.2

Multiply $2$ by $2$ .

$y = \frac{x}{6} - \frac{2}{4} + \frac{π}{4}$

Step 2.3.3

Combine the numerators over the common denominator.

$y = \frac{x}{6} + \frac{- 2 + π}{4}$

Step 2.3.4

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{x}{6} + \frac{- 1 (2) + π}{4}$

Step 2.3.5

Factor $- 1$ out of $π$ .

$y = \frac{x}{6} + \frac{- 1 (2) - 1 (- π)}{4}$

Step 2.3.6

Factor $- 1$ out of $- 1 (2) - 1 (- π)$ .

$y = \frac{x}{6} + \frac{- 1 (2 - π)}{4}$

Step 2.3.7

Move the negative in front of the fraction.

$y = \frac{x}{6} - \frac{2 - π}{4}$

Step 2.3.8

Reorder terms.

$y = \frac{1}{6} x - \frac{2 - π}{4}$