Precalculus Examples

$x = 3 (4)$ , $y = 2 - 4$

Step 1

When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is $y = k x$ , where $k$ is the constant of variation.

$y = k x$

Step 2

Solve the equation for $k$ , the constant of variation.

$k = \frac{y}{x}$

Step 3

Replace the variables $x$ and $y$ with the actual values.

$k = \frac{2 - 4}{3 (4)}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of $2 - 4$ and $4$ .

Tap for more steps...

Step 4.1.1

Factor $2$ out of $2$ .

$k = \frac{2 (1) - 4}{3 (4)}$

Step 4.1.2

Factor $2$ out of $- 4$ .

$k = \frac{2 \cdot 1 + 2 \cdot - 2}{3 (4)}$

Step 4.1.3

Factor $2$ out of $2 \cdot 1 + 2 \cdot - 2$ .

$k = \frac{2 \cdot (1 - 2)}{3 (4)}$

Step 4.1.4

Cancel the common factors.

Tap for more steps...

Step 4.1.4.1

Factor $2$ out of $3 (4)$ .

$k = \frac{2 \cdot (1 - 2)}{2 (3 \cdot (2))}$

Step 4.1.4.2

Cancel the common factor.

$k = \frac{2 \cdot (1 - 2)}{2 (3 \cdot (2))}$

Step 4.1.4.3

Rewrite the expression.

$k = \frac{1 - 2}{3 \cdot (2)}$

Step 4.2

Subtract $2$ from $1$ .

$k = \frac{- 1}{3 \cdot (2)}$

Step 5

Multiply $3$ by $2$ .

$k = \frac{- 1}{6}$

Step 6

Move the negative in front of the fraction.

$k = - \frac{1}{6}$