Question

The distance a car travels, in miles, can be found by the equation d = 45t, where t is measured in hours. Find the value of k (constant of proportionality) that best represents the situation.

A. The value of k is 45.
B. The value of k is 1/45.
C. The value of k is 0.
D. The value of k depends on the specific car used.

Answer 1

The constant of proportionality (k) in the equation d = 45t, representing the distance a car travels in miles per hour, is 45. This corresponds to option A.

Step-by-step explanation:

The constant of proportionality (k) in the equation d = 45t represents the rate at which distance is covered per unit of time. In this equation, distance is directly proportional to time, which means as time increases, the distance traveled also increases at a constant rate. Therefore, the constant of proportionality (k) is the coefficient of t, which in this instance is 45. This means that the car travels 45 miles for every hour of travel. Option A, that the value of k is 45, best represents the situation as it shows the distance traveled per hour.