Linear Algebra Examples

x = - 8

$x = - 8$ ,

y = 4

$y = 4$

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

$y = k x$ , 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{4}{- 8}

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

Step 4

Cancel the common factor of

4

$4$ and

- 8

$- 8$ .

Tap for more steps...

Step 4.1

Factor

4

$4$ out of

4

$4$ .

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

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

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor

4

$4$ out of

- 8

$- 8$ .

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

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

Step 4.2.2

Cancel the common factor.

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

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

Step 4.2.3

Rewrite the expression.

k = \frac{1}{- 2}

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

k = \frac{1}{- 2}

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

k = \frac{1}{- 2}

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

Step 5

Move the negative in front of the fraction.

k = - \frac{1}{2}

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

Step 6

Use the direct variation model to create the equation.

y = k x

$y = k x$

Step 7

Substitute the value of

k

$k$ into the direct variation model.

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

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

Step 8

Simplify the result to find the direct variation equation.

y = - \frac{x}{2}

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