Yes, p = 6m + 9m is an example of a proportional relationship.
Here's a step-by-step explanation:
Step 1: In the given equation, we can add the coefficients of 'm' since they are like terms. The equation becomes: p = 15m.
Step 2: This simplified equation represents a proportional relationship, as 'p' is equal to 15 times 'm'. That means that 'p' is directly proportional to 'm'.
Step 3: We can infer this because the ratio of 'p' to 'm' is constant, which is equal to the coefficient of 'm' in the simplified equation. In this case, the ratio p/m = 15 persists for every 'm' and the rate of change is consistent.
Step 4: This consistency in the rate of change, that is, for every increase in 'm', 'p' increases by a factor of 15, indicates a proportional relationship.
So, by looking at the characteristics of the given equation, we can confidently say that yes, p = 6m + 9m exemplifies a proportional relationship. This also means p=15m is the equation of direct variation for the given problem.