Summarize It! 1. Construct and Present Arguments A distance-time graph shows the motion of two bicycle riders. Each rider's motion is represented on the graph by a diagonal line sloping upward from left to right. The graph shows that they traveled the same distance. However, the line representing the motion of Rider \#1 slopes upward more steeply than the line representing the motion of Rider \#2. Sketch a graphical model of the motions of the riders. Develop an argument on which rider arrived at his or her destination first. How do you know? Use evidence to add validity to your argument.
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Rider #1 clearly made it to the finish line first! The steepness of Rider #1’s line on the distance-time graph indicates a faster speed compared to Rider #2. Since both riders traveled the same distance, the one with the steeper line, or the greater slope, covered that distance in a shorter amount of time. Therefore, while they may have ended up at the same point, Rider #1 took less time to get there! To visually demonstrate this, sketch two diagonal lines on a graph representing distance on the y-axis and time on the x-axis. Make Rider #1's line steeper than Rider #2's. This clear visual will help anyone see how time and distance are related, reinforcing that steeper lines indicate faster motion – and proving Rider #1’s speedy arrival!