Final answer:
Proportional relationship analysis focuses on constant rate of change: directly proportional relationships have a linear equation with a zero y-intercept, while inverse proportional relationships involve a variable increasing as another decreases.
Step-by-step explanation:
When analyzing whether a scenario presents a proportional relationship, we look for a constant rate of change between two variables. A directly proportional relationship means that as one variable increases, the other variable increases at a constant rate, and this can be represented by the equation y = kx, where k is the proportionality constant and the graph of the relationship will be a straight line through the origin (0, 0).
An inverse proportional relationship, on the other hand, exists when one variable increases as the other decreases, represented by the equation y = k/x. In this case, the graph will not be a straight line, and the relationship is not linear.
For a relationship to be considered proportional, it must follow the form of a linear equation y = mx + b, where m is the slope and b is the y-intercept, and specifically for direct proportionality, b must be zero. Hence, a linear relationship with a non-zero y-intercept does not represent a direct proportional relationship.