Calculus Examples

$y - 8 \sqrt{5} = \frac{\sqrt{5}}{5} (x - 8)$

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 $\frac{\sqrt{5}}{5} (x - 8)$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$y - 8 \sqrt{5} = \frac{\sqrt{5}}{5} x + \frac{\sqrt{5}}{5} \cdot - 8$

Step 2.1.1.1.2

Combine $\frac{\sqrt{5}}{5}$ and $x$ .

$y - 8 \sqrt{5} = \frac{\sqrt{5} x}{5} + \frac{\sqrt{5}}{5} \cdot - 8$

Step 2.1.1.1.3

Combine $\frac{\sqrt{5}}{5}$ and $- 8$ .

$y - 8 \sqrt{5} = \frac{\sqrt{5} x}{5} + \frac{\sqrt{5} \cdot - 8}{5}$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Move $- 8$ to the left of $\sqrt{5}$ .

$y - 8 \sqrt{5} = \frac{\sqrt{5} x}{5} + \frac{- 8 \sqrt{5}}{5}$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$y - 8 \sqrt{5} = \frac{\sqrt{5} x}{5} - \frac{8 \sqrt{5}}{5}$

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 $8 \sqrt{5}$ to both sides of the equation.

$y = \frac{\sqrt{5} x}{5} - \frac{8 \sqrt{5}}{5} + 8 \sqrt{5}$

Step 2.2.2

To write $8 \sqrt{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{\sqrt{5} x}{5} - \frac{8 \sqrt{5}}{5} + 8 \sqrt{5} \cdot \frac{5}{5}$

Step 2.2.3

Combine $8 \sqrt{5}$ and $\frac{5}{5}$ .

$y = \frac{\sqrt{5} x}{5} - \frac{8 \sqrt{5}}{5} + \frac{8 \sqrt{5} \cdot 5}{5}$

Step 2.2.4

Combine the numerators over the common denominator.

$y = \frac{\sqrt{5} x}{5} + \frac{- 8 \sqrt{5} + 8 \sqrt{5} \cdot 5}{5}$

Step 2.2.5

Combine the numerators over the common denominator.

$y = \frac{\sqrt{5} x - 8 \sqrt{5} + 8 \sqrt{5} \cdot 5}{5}$

Step 2.2.6

Multiply $5$ by $8$ .

$y = \frac{\sqrt{5} x - 8 \sqrt{5} + 40 \sqrt{5}}{5}$

Step 2.2.7

Add $- 8 \sqrt{5}$ and $40 \sqrt{5}$ .

$y = \frac{\sqrt{5} x + 32 \sqrt{5}}{5}$

Step 2.2.8

Split the fraction $\frac{\sqrt{5} x + 32 \sqrt{5}}{5}$ into two fractions.

$y = \frac{\sqrt{5} x}{5} + \frac{32 \sqrt{5}}{5}$

Step 2.3

Reorder terms.

$y = \frac{\sqrt{5}}{5} x + \frac{32 \sqrt{5}}{5}$