Algebra Examples

$x = 3$ , $y = \frac{2}{3}$

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.

$k = \frac{\frac{2}{3}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$k = \frac{2}{3} \cdot \frac{1}{3}$

Step 5

Multiply $\frac{2}{3} \cdot \frac{1}{3}$ .

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Step 5.1

Multiply $\frac{2}{3}$ by $\frac{1}{3}$ .

$k = \frac{2}{3 \cdot 3}$

Step 5.2

Multiply $3$ by $3$ .

$k = \frac{2}{9}$

Step 6

Use the direct variation model to create the equation.

$y = k x$

Step 7

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

$y = (\frac{2}{9}) x$

Step 8

Simplify the result to find the direct variation equation.

$y = \frac{2 x}{9}$