Question number 17. Each of five runners ran his or her distance at a constant speed. The results were plotted on a coordinate grid as shown. Who ran the fastest? So we have here on the horizontal axis time and distance on the vertical axis, and the results of each of the five runners are emphasized here with a dot. So the question is about the fastest speed, the fastest rate. So let's recall that distance traveled is equal to the speed times time. And what we are looking for is information about the speed, so we can solve for speed and say that distance divided by time is equal to speed. And looking at our graph here, the distance could be thought of as the quantity on the y-axis, and the time as the quantity on the x-axis. So we have that, in fact, speed here can be thought of as the change in y, and the time as the change in x. And so that is the slope. So let's draw back the slope of a line here through one of these points, and the origin here, which is emphasized in red here and called O. So let's draw some of these lines. So we have, in red here, the line that connects the origin to Beatrice, then to Daniel, then to Caesar, to Ernest, and finally to Anna, like that. And our question is to determine the fastest runner, so to find the greatest speed. And we see here that the greatest speed would correspond to the largest value of this fraction over here, so that, in fact, would be equal to the steepest slope. Greatest speed and the steepest slope are related. And so we see that the line that is most vertical, or closest to the y-axis, would be this line here, the first one we encounter, off vertical, and that corresponds to Daniel. So Daniel's line is the steepest, therefore he has the largest slope and is running at the fastest rate. So the answer here is Daniel, D.

fastest runner

slope of line

speed calculation

steepest slope

Daniel