Algebra Examples

$x = 10$ $y = 8$

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.

$k = \frac{8}{10}$

Step 4

Cancel the common factor of $8$ and $10$ .

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Step 4.1

Factor $2$ out of $8$ .

$k = \frac{2 (4)}{10}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $10$ .

$k = \frac{2 \cdot 4}{2 \cdot 5}$

Step 4.2.2

Cancel the common factor.

$k = \frac{2 \cdot 4}{2 \cdot 5}$

Step 4.2.3

Rewrite the expression.

$k = \frac{4}{5}$

Step 5

Use the direct variation model to create the equation.

$y = k x$

Step 6

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

$y = (\frac{4}{5}) x$

Step 7

Simplify the result to find the direct variation equation.

$y = \frac{4 x}{5}$