Calculus Examples

$y - \frac{1}{2} = \frac{19}{4} (x - 2)$

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 $\frac{19}{4} (x - 2)$ .

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Step 2.1.1.1

Apply the distributive property.

$y - \frac{1}{2} = \frac{19}{4} x + \frac{19}{4} \cdot - 2$

Step 2.1.1.2

Combine $\frac{19}{4}$ and $x$ .

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19}{4} \cdot - 2$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $4$ .

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19}{2 (2)} \cdot - 2$

Step 2.1.1.3.2

Factor $2$ out of $- 2$ .

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 2.1.1.3.3

Cancel the common factor.

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19}{2 \cdot 2} \cdot (2 \cdot - 1)$

Step 2.1.1.3.4

Rewrite the expression.

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19}{2} \cdot - 1$

Step 2.1.1.4

Combine $\frac{19}{2}$ and $- 1$ .

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{19 \cdot - 1}{2}$

Step 2.1.1.5

Simplify the expression.

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Step 2.1.1.5.1

Multiply $19$ by $- 1$ .

$y - \frac{1}{2} = \frac{19 x}{4} + \frac{- 19}{2}$

Step 2.1.1.5.2

Move the negative in front of the fraction.

$y - \frac{1}{2} = \frac{19 x}{4} - \frac{19}{2}$

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 $\frac{1}{2}$ to both sides of the equation.

$y = \frac{19 x}{4} - \frac{19}{2} + \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$y = \frac{19 x}{4} + \frac{- 19 + 1}{2}$

Step 2.2.3

Add $- 19$ and $1$ .

$y = \frac{19 x}{4} + \frac{- 18}{2}$

Step 2.2.4

Divide $- 18$ by $2$ .

$y = \frac{19 x}{4} - 9$

Step 2.3

Reorder terms.

$y = \frac{19}{4} x - 9$