Calculus Examples

$y - 4 = - \frac{1}{10} \cdot (x - 2)$

Step 1

Simplify $- \frac{1}{10} \cdot (x - 2)$ .

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Step 1.1

Rewrite.

$y - 4 = 0 + 0 - \frac{1}{10} \cdot (x - 2)$

Step 1.2

Simplify by adding zeros.

$y - 4 = - \frac{1}{10} \cdot (x - 2)$

Step 1.3

Apply the distributive property.

$y - 4 = - \frac{1}{10} x - \frac{1}{10} \cdot - 2$

Step 1.4

Combine $x$ and $\frac{1}{10}$ .

$y - 4 = - \frac{x}{10} - \frac{1}{10} \cdot - 2$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{10}$ into the numerator.

$y - 4 = - \frac{x}{10} + \frac{- 1}{10} \cdot - 2$

Step 1.5.2

Factor $2$ out of $10$ .

$y - 4 = - \frac{x}{10} + \frac{- 1}{2 (5)} \cdot - 2$

Step 1.5.3

Factor $2$ out of $- 2$ .

$y - 4 = - \frac{x}{10} + \frac{- 1}{2 \cdot 5} \cdot (2 \cdot - 1)$

Step 1.5.4

Cancel the common factor.

$y - 4 = - \frac{x}{10} + \frac{- 1}{2 \cdot 5} \cdot (2 \cdot - 1)$

Step 1.5.5

Rewrite the expression.

$y - 4 = - \frac{x}{10} + \frac{- 1}{5} \cdot - 1$

Step 1.6

Combine $\frac{- 1}{5}$ and $- 1$ .

$y - 4 = - \frac{x}{10} + \frac{- - 1}{5}$

Step 1.7

Multiply $- 1$ by $- 1$ .

$y - 4 = - \frac{x}{10} + \frac{1}{5}$

Step 2

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

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Step 2.1

Add $4$ to both sides of the equation.

$y = - \frac{x}{10} + \frac{1}{5} + 4$

Step 2.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{x}{10} + \frac{1}{5} + 4 \cdot \frac{5}{5}$

Step 2.3

Combine $4$ and $\frac{5}{5}$ .

$y = - \frac{x}{10} + \frac{1}{5} + \frac{4 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{10} + \frac{1 + 4 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $5$ .

$y = - \frac{x}{10} + \frac{1 + 20}{5}$

Step 2.5.2

Add $1$ and $20$ .

$y = - \frac{x}{10} + \frac{21}{5}$