Calculus Examples

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

Step 1

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

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Step 1.1

Rewrite.

$y - 1 = 0 + 0 + \frac{1}{2} \cdot (x - 1)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Move the negative in front of the fraction.

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

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $1$ to both sides of the equation.

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

Step 2.2

Write $1$ as a fraction with a common denominator.

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Add $- 1$ and $2$ .

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