1. The problem is to determine if $a = 500$ given that $y = 500$ when $c = 0$. 2. Typically, in a linear equation of the form $y = ac + b$, when $c = 0$, $y$ equals the constant term $b$. 3. If the equation is $y = ac + b$ and $y = 500$ when $c = 0$, then $500 = a \times 0 + b$ which simplifies to $b = 500$. 4. Therefore, $a$ is not necessarily 500; instead, $b$ equals 500. 5. Without additional information about the relationship between $a$, $c$, and $y$, we cannot conclude that $a = 500$. 6. In summary, $y = 500$ at $c = 0$ implies $b = 500$, not $a = 500$.