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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.

Ask by Harper West. in the United States
Jan 24,2025

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Answer

Rider #1 arrived at the destination first because their steeper slope on the distance-time graph indicates they traveled faster.

Solution

**Summary:** The problem involves analyzing a distance-time graph that depicts the movements of two bicycle riders, Rider #1 and Rider #2. Both riders travel the same distance, represented by diagonal lines rising from left to right on the graph. However, Rider #1's line has a steeper slope compared to Rider #2's line. The task is to: 1. **Sketch the Graphical Model:** Draw the distance-time graph illustrating both riders' motions, highlighting the difference in slopes. 2. **Develop an Argument:** Determine which rider reached the destination first based on the graph. 3. **Provide Evidence:** Use the slope differences as evidence to support the conclusion about which rider arrived first. **Key Points:** - Steeper slope indicates a faster rate of travel. - Since Rider #1 has a steeper slope, they maintained a higher speed. - Therefore, Rider #1 likely arrived at the destination before Rider #2.

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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!

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