Final answer:
The relationship between miles traveled and time on a bus traveling at 50 mph is an example of direct variation, with the equation N = 50t, where 50 is the constant of variation.
Step-by-step explanation:
The relationship between the number of miles traveled, N, and the time traveled, t hours, when traveling at a constant speed, is an example of direct variation. In direct variation, as one variable increases, the other variable increases at a constant rate. Here, if you travel at a speed of 50 mph, the number of miles traveled after t hours is N = 50t. This equation represents a direct variation because for every additional hour traveled, the distance N increases by 50 miles.
In direct variation, the equation can be written in the form y = kx, where k is the constant of variation. In this case, 50 is the constant of variation, and it represents the speed of the bus in miles per hour. The formula satisfies the condition of direct variation because there is a constant rate of change between time t and distance N, with no additional terms to complicate the relationship.