The given equation for the value of the baseball card in dollars is:
\[ 0.15y + 0.35 \]
In this equation, \(y\) represents the number of years since the baseball card was released. The term \(0.15y\) indicates that for each additional year \(y\), the value of the baseball card increases by \(0.15\) dollars.
Thus, the baseball card's value is increasing by:
\[ \boxed{0.15} \text{ dollars per year.} \]