Calculus Examples

$y + 2 = - \frac{1}{7} \cdot (x - 2)$

Step 1

Simplify $- \frac{1}{7} \cdot (x - 2)$ .

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Step 1.1

Rewrite.

$y + 2 = 0 + 0 - \frac{1}{7} \cdot (x - 2)$

Step 1.2

Simplify by adding zeros.

$y + 2 = - \frac{1}{7} \cdot (x - 2)$

Step 1.3

Apply the distributive property.

$y + 2 = - \frac{1}{7} x - \frac{1}{7} \cdot - 2$

Step 1.4

Combine $x$ and $\frac{1}{7}$ .

$y + 2 = - \frac{x}{7} - \frac{1}{7} \cdot - 2$

Step 1.5

Multiply $- \frac{1}{7} \cdot - 2$ .

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Step 1.5.1

Multiply $- 2$ by $- 1$ .

$y + 2 = - \frac{x}{7} + 2 (\frac{1}{7})$

Step 1.5.2

Combine $2$ and $\frac{1}{7}$ .

$y + 2 = - \frac{x}{7} + \frac{2}{7}$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$y = - \frac{x}{7} + \frac{2}{7} - 2$

Step 2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = - \frac{x}{7} + \frac{2}{7} - 2 \cdot \frac{7}{7}$

Step 2.3

Combine $- 2$ and $\frac{7}{7}$ .

$y = - \frac{x}{7} + \frac{2}{7} + \frac{- 2 \cdot 7}{7}$

Step 2.4

Combine the numerators over the common denominator.

$y = - \frac{x}{7} + \frac{2 - 2 \cdot 7}{7}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $7$ .

$y = - \frac{x}{7} + \frac{2 - 14}{7}$

Step 2.5.2

Subtract $14$ from $2$ .

$y = - \frac{x}{7} + \frac{- 12}{7}$

Step 2.6

Move the negative in front of the fraction.

$y = - \frac{x}{7} - \frac{12}{7}$