To determine the equation that models the proportional relationship between the number of nonconference games (denoted as [tex]\( y \)[/tex]) and the number of conference games (denoted as [tex]\( x \)[/tex]), we need to understand the ratio provided: 2 nonconference games for every 3 conference games.
Given this ratio, we can express the relationship as follows:
[tex]\[
\frac{y}{x} = \frac{2}{3}
\][/tex]
This equation tells us that for every 3 conference games, there are 2 nonconference games. To express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we multiply both sides of the equation by [tex]\( x \)[/tex]:
[tex]\[
y = \frac{2}{3} x
\][/tex]
Thus, the correct equation that models the relationship between nonconference games and conference games is:
[tex]\[
y = \frac{2}{3} x
\][/tex]
So, the equation that best fits this proportional relationship is:
[tex]\[
\boxed{y = \frac{2}{3} x}
\][/tex]
