A GPS device tracks the elevation

Question

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure.

Repeat the procedure outlined in part (a) for the secant line that passes through points $P$ and $Q$ .

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with finding the slope of a line. This problem says a car travels along a straight road and its distance D in miles from the starting point is recorded every hour. The distance traveled two hours after the journey began is recorded. A second line that passes through the points C and D is drawn, determine the slope of this line and interpret it as an average rate of change over the interval of six is less than or equal to T is less than or equal to seven. Below the question. We're given a graph, the hazard distance D along the Y axis and our time T along the X axis. On the graph, there is a curve and on this curve, there are points that are labeled at one hour intervals. There's also a line that is connecting point C and D on a graph and point C has a value of six comma 648 and point D has a value of seven comma 609. We're also given four possible choices as our answers. For choice. A we have 38 MPH. The car moves away from the starting point at an average rate of 38 MPH. For choice. B we have minus 38 MPH. The car moves towards the starting point at an average rate of 38 MPH. For choice C we have 39 MPH. The car moves away from the starting point at an average rate of 39 MPH. And for choice D, we have minus 39 MPH. Car moves towards the starting point at an average rate of 39 MPH. Now, the first part of this question wants us to find the slope of the second line that is connecting points C and D. So in order to find that slope, I need to actually find the values of those two points. Now, for point C that occurs when our value of T is equal to six hours. And the distance that is covered during that time or recorded at that time will label as D of six, it's gonna be equal to 648 miles. And so that is just being read off the graph. Since our point C has a value of six comma 648 we'll do the same thing for point D, point D occurs at T is equal to seven. And so we'll have D of seven and that's gonna be equal to 609. Again, just reading that directly off of the graph. Now recall your definition of a slope, your slope is equal to your change in Y divided by your change in X. That means that our slope M is going to be equal to, for our change in why? That is going to be 609 minus 648. That's gonna be divided by R change in X which is seven minus six. And so when I plug those values to my calculator, I'll get m it's equal to minus 39 MPH. So the units here come out to be MPH because our numerator has units of miles. That's what our distance was measured in. And our denominator had units of hours since that's what our time was measured in. So that is the first half of our answer. The second half asked us to interpret this as a rate of change, average rate of change over the interval between six and seven hours. So this slope here is actually negative. So that means my distance is decreasing with time. So I'm actually getting closer to the starting point. And so this means that the car is actually moving towards the starting point at an average rate of 39 MPH. It's an average rate since I just used R two end points. So with that interpretation in mind, I can come down and look at my answer choices and the correct answer choice actually corresponds to answer choice D because the slope has a value of minus 39 MPH. And the interpretation is that the car moves towards the starting point at an average rate of 39 MPH. So I hope that this explanation has been useful and I'll see you in the next video.

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>
Repeat the procedure outlined in part (a) for the secant line that passes through points $P$ and $Q$ .

Key Concepts

Secant Line

Average Rate of Change

Function Representation

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