Precalculus Examples

$y - (6) = - \frac{2}{3} \cdot (x - (- 8))$

Step 1

Multiply $- 1$ by $6$ .

$y - 6 = - \frac{2}{3} \cdot (x - (- 8))$

Step 2

Simplify $- \frac{2}{3} \cdot (x - (- 8))$ .

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Step 2.1

Multiply $- 1$ by $- 8$ .

$y - 6 = - \frac{2}{3} \cdot (x + 8)$

Step 2.2

Apply the distributive property.

$y - 6 = - \frac{2}{3} x - \frac{2}{3} \cdot 8$

Step 2.3

Combine $x$ and $\frac{2}{3}$ .

$y - 6 = - \frac{x \cdot 2}{3} - \frac{2}{3} \cdot 8$

Step 2.4

Multiply $- \frac{2}{3} \cdot 8$ .

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Step 2.4.1

Multiply $8$ by $- 1$ .

$y - 6 = - \frac{x \cdot 2}{3} - 8 (\frac{2}{3})$

Step 2.4.2

Combine $- 8$ and $\frac{2}{3}$ .

$y - 6 = - \frac{x \cdot 2}{3} + \frac{- 8 \cdot 2}{3}$

Step 2.4.3

Multiply $- 8$ by $2$ .

$y - 6 = - \frac{x \cdot 2}{3} + \frac{- 16}{3}$

Step 2.5

Simplify each term.

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Step 2.5.1

Move $2$ to the left of $x$ .

$y - 6 = - \frac{2 \cdot x}{3} + \frac{- 16}{3}$

Step 2.5.2

Move the negative in front of the fraction.

$y - 6 = - \frac{2 x}{3} - \frac{16}{3}$

Step 3

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

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Step 3.1

Add $6$ to both sides of the equation.

$y = - \frac{2 x}{3} - \frac{16}{3} + 6$

Step 3.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{2 x}{3} - \frac{16}{3} + 6 \cdot \frac{3}{3}$

Step 3.3

Combine $6$ and $\frac{3}{3}$ .

$y = - \frac{2 x}{3} - \frac{16}{3} + \frac{6 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$y = - \frac{2 x}{3} + \frac{- 16 + 6 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $6$ by $3$ .

$y = - \frac{2 x}{3} + \frac{- 16 + 18}{3}$

Step 3.5.2

Add $- 16$ and $18$ .

$y = - \frac{2 x}{3} + \frac{2}{3}$