Calculus Examples

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

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 $\frac{\sqrt{2}}{2} (x - 1)$ .

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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.

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

Step 2.1.1.1.2

Combine $\frac{\sqrt{2}}{2}$ and $x$ .

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

Step 2.1.1.1.3

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

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

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

Simplify the numerator.

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Step 2.1.1.2.1.1

Move $- 1$ to the left of $\sqrt{2}$ .

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

Step 2.1.1.2.1.2

Rewrite $- 1 \sqrt{2}$ as $- \sqrt{2}$ .

$y - \sqrt{2} = \frac{\sqrt{2} x}{2} + \frac{- \sqrt{2}}{2}$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$y - \sqrt{2} = \frac{\sqrt{2} x}{2} - \frac{\sqrt{2}}{2}$

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

$y = \frac{\sqrt{2} x}{2} - \frac{\sqrt{2}}{2} + \sqrt{2}$

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Combine the numerators over the common denominator.

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

Step 2.2.5

Combine the numerators over the common denominator.

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

Step 2.2.6

Move $2$ to the left of $\sqrt{2}$ .

$y = \frac{\sqrt{2} x - \sqrt{2} + 2 \sqrt{2}}{2}$

Step 2.2.7

Add $- \sqrt{2}$ and $2 \sqrt{2}$ .

$y = \frac{\sqrt{2} x + \sqrt{2}}{2}$

Step 2.2.8

Split the fraction $\frac{\sqrt{2} x + \sqrt{2}}{2}$ into two fractions.

$y = \frac{\sqrt{2} x}{2} + \frac{\sqrt{2}}{2}$

Step 2.3

Reorder terms.

$y = \frac{\sqrt{2}}{2} x + \frac{\sqrt{2}}{2}$