Algebra Examples

$x = - 5$ , $y = \frac{3}{4}$

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.

$k = \frac{\frac{3}{4}}{- 5}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$k = \frac{3}{4} \cdot \frac{1}{- 5}$

Step 5

Move the negative in front of the fraction.

$k = \frac{3}{4} \cdot (- \frac{1}{5})$

Step 6

Multiply $\frac{3}{4} (- \frac{1}{5})$ .

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Step 6.1

Multiply $\frac{3}{4}$ by $\frac{1}{5}$ .

$k = - \frac{3}{4 \cdot 5}$

Step 6.2

Multiply $4$ by $5$ .

$k = - \frac{3}{20}$

Step 7

Use the direct variation model to create the equation.

$y = k x$

Step 8

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

$y = (- \frac{3}{20}) \cdot x$

Step 9

Simplify the result to find the direct variation equation.

$y = - \frac{3 x}{20}$