Final answer:
The relationship between the total hours studied and the number of weeks studied, when proportional, is represented by the equation y = kx, where k is the constant of proportionality determined by the number of hours studied per week.
Step-by-step explanation:
The relationship you're describing where the total hours studied is proportional to the number of weeks studied indicates that we're dealing with a directly proportional relationship. In such a case, the equation that would represent y, the total number of hours studied, in terms of x, the number of weeks, would be y = kx, where k is the proportionality constant.
To determine this equation, you need to know how many hours are studied in one week to find the value of k. For example, if you studied 5 hours in one week, then k would be 5, and your equation would be y = 5x. This means for each week studied, you study 5 hours, so the total hours studied would be 5 times the number of weeks. This relationship would produce a straight line on a graph that passes through the origin (0, 0), illustrating that the variables increase where increasing weeks will always result in a corresponding increase in total hours studied at the same rate.