Algebra Examples

$y = 4$ $x = 10$

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.

$y = k x$

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

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

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

$k = \frac{4}{10}$

Cancel the common factor of $4$ and $10$ .

Tap for more steps...

Factor $2$ out of $4$ .

$k = \frac{2 (2)}{10}$

Cancel the common factors.

Tap for more steps...

Factor $2$ out of $10$ .

$k = \frac{2 \cdot 2}{2 \cdot 5}$

Cancel the common factor.

$k = \frac{2 \cdot 2}{2 \cdot 5}$

Rewrite the expression.

$k = \frac{2}{5}$

Use the direct variation model to create the equation.

$y = k x$

Substitute the value of $k$ into the direct variation model.

$y = (\frac{2}{5}) x$

Simplify the result to find the direct variation equation.

$y = \frac{2 x}{5}$