Note: For question 15, your teacher will grade your responses to ensure you receive proper credit for your answers.
Juan and Rita both rode bicycles from the park to Main Street. The graphs below represent the time and distance for each student’s ride. Who rode more slowly? Justify your answer.
A coordinate graph for Rita is shown.The horizontal axis is labeled Time in minutes and is scaled from 0 to 20 by 2.
The vertical axis is labeled Distance in blocks and is scaled from 0 to 10 by 1.
There are points at left parenthesis 0 comma 0 right parenthesis, left parenthesis 2 comma 2 right parenthesis, left parenthesis 4 comma 4 right parenthesis, left parenthesis 6 comma 6 right parenthesis, and left parenthesis 8 comma 8 right parenthesis connected by line segments. A coordinate graph for Juan is shown.The horizontal axis is labeled Time in minutes and scaled from 0 to 20 by 2.
The vertical axis is labeled Distance in blocks and scaled from 0 to 10 by 1.
There are points at left-parenthesis 0 comma 0 right-parenthesis, left-parenthesis 5 comma 2 right-parenthesis, left-parenthesis 8 comma 4 right-parenthesis, left-parenthesis 12 comma 6 right-parenthesis, and left-parenthesis 17 comma 8 right-parenthesis connected by line segments.
this is so easy but you gotta do what you gotta do
Based on the graphs, it appears that Rita rode more slowly than Juan. This is because her line segments are at a shallower slope, indicating that she covered less distance in the same amount of time compared to Juan's steeper line segments. Additionally, at the 8-minute mark, Juan was at the 4-block distance mark, while Rita was only at the 2-block distance mark, further indicating that she was slower.
learn how to type math, and we'll talk.
To determine who rode more slowly, we need to compare the slopes of the lines on the coordinate graphs. The slope represents the rate of change of distance with respect to time.
Looking at the graph for Rita, the line passes through the points (0,0), (2,2), (4,4), (6,6), and (8,8). The distance increases by 2 blocks every 2 minutes, indicating a slope of 2/2 = 1 block per minute.
On the other hand, the graph for Juan passes through the points (0,0), (5,2), (8,4), (12,6), and (17,8). The distance increases by 2 blocks every 5 minutes, indicating a slope of 2/5 = 0.4 blocks per minute.
Comparing the slopes, we can see that Rita rode more slowly as she had a slope of 1 block per minute while Juan had a slope of 0.4 blocks per minute.
To determine who rode more slowly, we need to compare the slopes of the two graphs. The slope represents the rate of change.
Let's begin with Rita's graph. The points on her graph are (0,0), (2,2), (4,4), (6,6), and (8,8). To calculate the slope, we need to find the change in distance divided by the corresponding change in time.
For the first segment, the change in distance is 2 blocks (from 0 to 2) and the change in time is 2 minutes. So, the slope for the first segment is 2/2 = 1.
We can repeat this process for the other segments and find that the slope for each segment is also 1.
Now, let's move on to Juan's graph. The points on his graph are (0,0), (5,2), (8,4), (12,6), and (17,8). Again, we need to calculate the slope for each segment.
For the first segment, the change in distance is 2 blocks (from 0 to 2) and the change in time is 5 minutes. So, the slope for the first segment is 2/5.
Continuing this process for the other segments, we find that the slopes for Juan's graph are 2/5, 2/4, 2/4, and 2/5.
Comparing the slopes, we can see that Rita's slope is constant at 1, while Juan's slopes vary between 2/5 and 2/4. This means that Juan rode more slowly than Rita because his slope is smaller.