Question
The graph shows the distance traveled by an Olympic-level sprinter over time during a race. Find the slope of the line. What does it represent?
image
A.
The slope of the line is 10. It tells the distance the sprinter traveled per second.
B.
The slope of the line is
1
2
. It telss the seconds it takes a sprinter to travel a certain distance
C.
The slope is 0. It tells the time it takes to travel 100 meters
D.
The slope is
20
2
. It tells the distance the sprinter traveled per second.
image
A.
The slope of the line is 10. It tells the distance the sprinter traveled per second.
B.
The slope of the line is
1
2
. It telss the seconds it takes a sprinter to travel a certain distance
C.
The slope is 0. It tells the time it takes to travel 100 meters
D.
The slope is
20
2
. It tells the distance the sprinter traveled per second.
Answers
GPT-4o mini
To determine the correct answer, we need to analyze the concept of slope in the context of the distance-time graph for the sprinter.
The slope of a line in a distance-time graph is calculated as the change in distance (rise) divided by the change in time (run). Mathematically, this is represented as:
\[ \text{slope} = \frac{\text{change in distance}}{\text{change in time}} \]
In the context of the race, the slope represents the speed or velocity of the sprinter. Specifically, if the slope is a positive number, it indicates how much distance the sprinter covers in a unit of time (for instance, meters per second).
Now let's evaluate the options:
- **A**. "The slope of the line is 10. It tells the distance the sprinter traveled per second."
- If the slope is 10, this would indicate that the sprinter travels 10 meters per second.
- **B**. "The slope of the line is 1/2. It tells the seconds it takes a sprinter to travel a certain distance."
- This is incorrect, as a slope of 1/2 would indicate the sprinter travels only 0.5 meters per second, not the time taken to travel any distance.
- **C**. "The slope is 0. It tells the time it takes to travel 100 meters."
- A slope of 0 would mean no distance is being covered, which is not the case for a sprinter.
- **D**. "The slope is 20/2. It tells the distance the sprinter traveled per second."
- This simplifies to 10, meaning the sprinter travels 10 meters per second, similar to option A.
From the analysis above, the most appropriate interpretation of the slope depends on the actual value.
If the slope of the line is indeed **10** (as in option A), then it correctly states that it represents the distance traveled per second. However, if it's simplified to **10** from option D (20/2 = 10), that too is correct.
Therefore, the best answer here, assuming we are to choose the most straightforward representation of the slope as a positive number, would be:
**A. The slope of the line is 10. It tells the distance the sprinter traveled per second.**
If it's not determined directly from the graph or the context, ensure to check the slope through the stated values from the image. These options clarify how to express that slope in relation to distance traveled per second.
The slope of a line in a distance-time graph is calculated as the change in distance (rise) divided by the change in time (run). Mathematically, this is represented as:
\[ \text{slope} = \frac{\text{change in distance}}{\text{change in time}} \]
In the context of the race, the slope represents the speed or velocity of the sprinter. Specifically, if the slope is a positive number, it indicates how much distance the sprinter covers in a unit of time (for instance, meters per second).
Now let's evaluate the options:
- **A**. "The slope of the line is 10. It tells the distance the sprinter traveled per second."
- If the slope is 10, this would indicate that the sprinter travels 10 meters per second.
- **B**. "The slope of the line is 1/2. It tells the seconds it takes a sprinter to travel a certain distance."
- This is incorrect, as a slope of 1/2 would indicate the sprinter travels only 0.5 meters per second, not the time taken to travel any distance.
- **C**. "The slope is 0. It tells the time it takes to travel 100 meters."
- A slope of 0 would mean no distance is being covered, which is not the case for a sprinter.
- **D**. "The slope is 20/2. It tells the distance the sprinter traveled per second."
- This simplifies to 10, meaning the sprinter travels 10 meters per second, similar to option A.
From the analysis above, the most appropriate interpretation of the slope depends on the actual value.
If the slope of the line is indeed **10** (as in option A), then it correctly states that it represents the distance traveled per second. However, if it's simplified to **10** from option D (20/2 = 10), that too is correct.
Therefore, the best answer here, assuming we are to choose the most straightforward representation of the slope as a positive number, would be:
**A. The slope of the line is 10. It tells the distance the sprinter traveled per second.**
If it's not determined directly from the graph or the context, ensure to check the slope through the stated values from the image. These options clarify how to express that slope in relation to distance traveled per second.