Problem 50 - College Algebra

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The graph of this direct variation equation that has a positive constant of variation shows one variable increasing as the other variable decreases.

Step-by-Step Solution

Answer

The statement does not make sense because in a direct variation, if one variable increases, the other variable also increases at a constant rate or vice versa. The statement suggests an inverse variation situation, not a direct variation.

Step 1: Understand the concept of Direct Variation

In a direct variation, when one variable increases, the other variable also increases at a constant rate or if one variable decreases, the other also decreases at a constant rate. The equation for a direct variation is generally of the form \(y=kx\), where \(k\) is the constant of variation.

Step 2: Analyze the statement

The statement says that we have a direct variation equation, where one variable increases as the other decreases. This is contradictory to the definition of direct variation, where both variables either increase or decrease together.

Step 3: Conclude

Since the statement contradicts the concept of direct variation, we can say that it does not make sense.