Conquer the College Math Placement Challenge 2026 – Step Up and Shine!

When we say that \( y \) varies inversely as \( x \), it means that the product of \( x \) and \( y \) is a constant. This relationship can be represented by the equation:

\[

xy = k

\]

where \( k \) is the constant.

In this problem, we are given specific values: \( x = 4 \) and \( y = 2 \). To find the constant \( k \), we substitute the values of \( x \) and \( y \) into the equation:

\[

4 \cdot 2 = k

\]

Calculating this gives us:

\[

k = 8

\]

Thus, the constant \( k \) when \( x = 4 \) and \( y = 2 \) is indeed 8. This means that regardless of the specific values of \( x \) and \( y \), their product will always equal 8 in this particular case of inverse variation.