Final answer:
The question about what must 'a' be for a function to be linear is missing specific details to provide a precise answer. Generally, a linear function has a constant rate of change, which would make 'a' a fixed number. However, without the full function, we can't determine 'a'. Also, in physics, a plot of displacement versus time that is linear means zero acceleration.
Step-by-step explanation:
The original question appears to be incomplete as it is referring to a variable 'a' and a function but does not provide the full context or equation in which 'a' is to be determined. However, broad principles can be applied to address what is typically needed for a function to be considered linear. A linear function has a constant rate of change, which is the coefficient of 'x' in the equation of the line. If a variable 'a' would directly determine this coefficient, 'a' must be a constant number to ensure the function is linear. Without the specific function, it's not possible to determine the exact value of 'a'. Moreover, options provided in the question seem to refer to a rate of change which suggests they are choices for the value of 'a'. But, without the function or additional context it's not possible to accurately select a correct option.
Switching context to the included information, a plot of displacement versus time being linear implies that acceleration is zero since the slope of the displacement-time graph represents velocity, and if this is constant (as indicated by a linear graph), acceleration must be zero. In physics, 'a' typically represents acceleration and is considered a constant in many types of motion as indicated, however, it's not clear how this relates to the original question about a linear function.