Question

One student says that the equation \(y=-2 x\) is an example of direct variation. Another student says it is inverse variation. Which is correct? Explain.

Short answer

The correct definition for the equation \(y = -2x\) is direct variation, because it adheres to the format \(y = kx\), where \(k\) is a constant, -2 in this case. When \(x\) increases, \(y\) decreases by a constant multiplier.

Step-by-step solution

Understanding Direct Variation

Direct variation is when the ratio between two variables remains constant. This relationship can be represented as \(y = kx\), where \(k\) is the constant of variation.

Understanding Inverse Variation

Inverse Variation is when the product of two variables is constant. This can be represented as \(y = k/x\), where \(k\) is the constant.

Analyzing the equation

The given equation, \(y = -2x\), is in the form of a direct variation equation, where the coefficient of \(x\), -2, serves as the constant of variation.