Final answer:
The constant of proportionality represents the rate at which two variables are directly proportional. In the equation y = 7.5x, the constant is 7.5, signifying that y increases by 7.5 for each unit increase in x.
Step-by-step explanation:
The constant of proportionality is the factor that relates two variables that are directly proportional to each other. In the equation provided by the student, y = 7.5x, the constant of proportionality is the coefficient of x, which in this case is 7.5.
This indicates that for every unit increase in x, the value of y increases by 7.5 units. This is similar to the example where the equation y = 55x + 75 has a constant of proportionality (or slope) of 55.
For the student's scenario with Julio riding his bike, we could write the equation as y = (7.5 miles/37.5 minutes) × t, representing the proportional relationship between the distance traveled (y) and the time (t), with the constant of proportionality being the speed at which Julio rides.