Question in description

Question

During a weekend trip riding his motorcycle. Neil plans to average 55 miles per hour.

a) What type of function would be a good model for this situation?

b) Sketch a graph representing the distance he will travel y in terms of the number of hours x that he rides.

c) Use the graph to identify the intercepts(s) and interpret the meaning of each intercept in the context of the situation.

Answer 1

Hello, Crystal,

Let D = Distance (in miles), Speed = S (in miles/hour), and T = Time (in hours)

The distance traveled is simply the speed (55 miles/hr) times the time

D = S*T, or D = 55*T

Since Neil travels for T = X, we can rephrase the equation: D = 55*X. We can rearrange to solve for either D or X. If Neil knows how long he was riding, he enters that values (in hours) for X. This is a straight line with a slope of 55 and an intercept of 0. You may be more familiar with the y=mx + b format. This is the same except we are using D instead of Y. The graph would be a straight line with an intercept at 0,0. . This intercept is simply where Neil started, at time 0. Distance would be miles and time is in hours.