Calculus Examples

$y - 3 = \frac{0 - 3}{- 9 - 9} (x - 9)$

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 $\frac{0 - 3}{- 9 - 9} (x - 9)$ .

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Step 2.1.1.1

Simplify by subtracting numbers.

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Step 2.1.1.1.1

Subtract $3$ from $0$ .

$y - 3 = \frac{- 3}{- 9 - 9} (x - 9)$

Step 2.1.1.1.2

Subtract $9$ from $- 9$ .

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

Step 2.1.1.2

Cancel the common factor of $- 3$ and $- 18$ .

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Step 2.1.1.2.1

Factor $- 3$ out of $- 3$ .

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

Step 2.1.1.2.2

Cancel the common factors.

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Step 2.1.1.2.2.1

Factor $- 3$ out of $- 18$ .

$y - 3 = \frac{- 3 \cdot 1}{- 3 \cdot 6} (x - 9)$

Step 2.1.1.2.2.2

Cancel the common factor.

$y - 3 = \frac{- 3 \cdot 1}{- 3 \cdot 6} (x - 9)$

Step 2.1.1.2.2.3

Rewrite the expression.

$y - 3 = \frac{1}{6} (x - 9)$

Step 2.1.1.3

Apply the distributive property.

$y - 3 = \frac{1}{6} x + \frac{1}{6} \cdot - 9$

Step 2.1.1.4

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

$y - 3 = \frac{x}{6} + \frac{1}{6} \cdot - 9$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Factor $3$ out of $6$ .

$y - 3 = \frac{x}{6} + \frac{1}{3 (2)} \cdot - 9$

Step 2.1.1.5.2

Factor $3$ out of $- 9$ .

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

Step 2.1.1.5.3

Cancel the common factor.

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

Step 2.1.1.5.4

Rewrite the expression.

$y - 3 = \frac{x}{6} + \frac{1}{2} \cdot - 3$

Step 2.1.1.6

Combine $\frac{1}{2}$ and $- 3$ .

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

Step 2.1.1.7

Move the negative in front of the fraction.

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

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 $3$ to both sides of the equation.

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $3$ by $2$ .

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

Step 2.2.5.2

Add $- 3$ and $6$ .

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

Step 2.3

Reorder terms.

$y = \frac{1}{6} x + \frac{3}{2}$