Final answer:
The relationship is proportional because the given equation is linear with a y-intercept of 0, indicating a constant ratio between distance and time which results in a straight line when graphed.
Step-by-step explanation:
To determine whether there is a proportional relationship between two quantities, we should check if the ratio between them is constant. In this case, the given equation is y = (2.0 km/min) t, which can be seen as y = mt + b where m is the slope (rate of change) and b is the y-intercept. When b = 0, as in this equation, it means the line goes through the origin (0,0) on a graph. This indicates a directly proportional relationship because as time (t) increases, the distance (y) increases at a constant rate.
For the relationship to be proportional, there should be a straight line when plotted on a graph. As per the information given, the equation y = (2.0 km/min) t + 0 implies a linear graph with a slope of 2.0 km/min and a y-intercept of 0. This satisfies the condition for a proportional relationship where the equation is of the form y = kx, and there is no constant term added (b = 0). Therefore, statement a) 'Yes, it is a proportional relationship because the ratio of distance to time is constant' is the correct answer.