Question

Does the equation model direct variation, inverse variation, or neither? $$x=\frac{4}{y}$$

Short answer

The equation \(x=\frac{4}{y}\) models an inverse variation.

Step-by-step solution

Identify the Form of the Given Equation

In the equation \(x=\frac{4}{y}\), it can be rewritten in a form where the product of two variables equals a constant. Multiply both sides by y to get \(xy=4\). Here, the constant is 4.

Analyze the Form of the Equation

The equation \(xy=4\) is in the form of an inverse variation, where the product of \(x\) and \(y\) is a constant. This is not in the form \(y=kx\) which is a direct variation.

Determining the Type of Variation

As the equation \(xy=4\) follows the inverse variation and not the direct variation, the given equation represents an inverse variation.