Linear Algebra Examples

$x = - 8$ ,

$y = 4$

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.

$k = \frac{4}{- 8}$

Step 4

Cancel the common factor of

$4$ and

$- 8$ .

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Step 4.1

Factor

$4$ out of

$4$ .

$k = \frac{4 (1)}{- 8}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

$4$ out of

$- 8$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$k = \frac{1}{- 2}$

Step 5

Move the negative in front of the fraction.

$k = - \frac{1}{2}$

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.

$y = (- \frac{1}{2}) \cdot x$

Step 8

Simplify the result to find the direct variation equation.

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