To express: The distance in terms of the time elapsed.
The distance d in terms of time elapsed is, .
Let d be the distance traveled in miles and the t be the time elapsed in hours.
When t = 0, the distance is 0 which can be expressed as (0, 0).
Since he passes the Ann Arbor at 50 minutes, t = 50 minutes or
The distance traveled is 40 miles. That is, at , which can be expressed as .
Use the obtained two points and find the slope m as follows.
Thus, the slope .
Use the slope and the point (0, 0) and obtain the equation of distance d in terms of time elapsed t as follows.
Thus, the required function is .
To sketch: The graph of the distance equation obtained in part (a).
Let x-axis be represented the time in hours and the y-axis be represented the distance in miles.
Given that the distance function of elapsed time is .
Obtain the value of d for various values of t and draw the graph of d as shown below in Figure 1.
From Figure 1, it is observed that function is a linear function.
To find: The slope of the graph drawn in part (b); explain the meaning of slope.
The slope is 48, which represents the rate of change of the distance in miles.
The equation is in the form of in which m is slope and c is the y-intercept.
Thus, the slope of the Figure 1 shown in part (b) is 48. It represents that the rate of change of the distance in miles.
Moreover, it is observed that there is a decrease in the distance when time increases and hence it is in direct variation. The distance covered in an hour is 48 miles.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!