Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

In inverse variation, how is y expressed in relation to x?

1. y = kx

2. y = k + x

3. y = k/x

4. y = x/k

The correct answer is: y = k/x

In inverse variation, the relationship between two variables, \( y \) and \( x \), is defined such that when one variable increases, the other decreases in a way that their product remains constant. This relationship can be expressed mathematically as \( y = \frac{k}{x} \), where \( k \) is a constant. This equation reflects the core concept of inverse variation: as \( x \) increases, \( y \) must decrease in order to keep their product \( k \) constant. Conversely, if \( x \) decreases, \( y \) will increase. The structure of the equation illustrates that \( y \) is inversely proportional to \( x \) because \( y \) varies with the reciprocal of \( x \). Other options do not represent an inverse relationship. For example, expressing \( y \) as \( kx \) indicates a direct variation, where both variables increase or decrease together. Similarly, \( y = k + x \) introduces a linear relationship, and \( y = \frac{x}{k} \) still suggests direct variation since \( y \) is directly proportional to \( x \). Thus, \( y = \frac{k}{x} \) is the only choice