Examples

y = 15

$y = 15$ ,

x = 10

$x = 10$ ,

x = 6

$x = 6$

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

$y = k x$ , where

k

$k$ is the constant of variation.

y = k x

$y = k x$

Step 2

Solve the equation for

k

$k$ , the constant of variation.

k = \frac{y}{x}

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

Step 3

Replace the variables

x

$x$ and

y

$y$ with the actual values.

k = \frac{15}{10}

$k = \frac{15}{10}$

Step 4

Cancel the common factor of

15

$15$ and

10

$10$ .

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Step 4.1

Factor

5

$5$ out of

15

$15$ .

k = \frac{5 (3)}{10}

$k = \frac{5 (3)}{10}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

5

$5$ out of

10

$10$ .

k = \frac{5 \cdot 3}{5 \cdot 2}

$k = \frac{5 \cdot 3}{5 \cdot 2}$

Step 4.2.2

Cancel the common factor.

k = \frac{5 \cdot 3}{5 \cdot 2}

$k = \frac{5 \cdot 3}{5 \cdot 2}$

Step 4.2.3

Rewrite the expression.

k = \frac{3}{2}

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

k = \frac{3}{2}

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

k = \frac{3}{2}

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

Step 5

Use the formula

y = k x

$y = k x$ to substitute

\frac{3}{2}

$\frac{3}{2}$ for

k

$k$ and

6

$6$ for

x

$x$ .

y = (\frac{3}{2}) \cdot (6)

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

Step 6

Solve for

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Step 6.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

6

$6$ .

y = \frac{3}{2} \cdot (6)

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

Step 6.2

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

6

$6$ .

y = \frac{3}{2} \cdot 6

$y = \frac{3}{2} \cdot 6$

Step 6.3

Remove parentheses.

y = (\frac{3}{2}) \cdot (6)

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

Step 6.4

Simplify

(\frac{3}{2}) \cdot (6)

$(\frac{3}{2}) \cdot (6)$ .

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Step 6.4.1

Cancel the common factor of

2

$2$ .

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Step 6.4.1.1

Factor

2

$2$ out of

6

$6$ .

y = \frac{3}{2} \cdot (2 (3))

$y = \frac{3}{2} \cdot (2 (3))$

Step 6.4.1.2

Cancel the common factor.

y = \frac{3}{2} \cdot (2 \cdot 3)

$y = \frac{3}{2} \cdot (2 \cdot 3)$

Step 6.4.1.3

Rewrite the expression.

y = 3 \cdot 3

$y = 3 \cdot 3$

y = 3 \cdot 3

$y = 3 \cdot 3$

Step 6.4.2

Multiply

3

$3$ by

3

$3$ .

y = 9

$y = 9$

y = 9

$y = 9$

y = 9

$y = 9$

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