Question
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Answers
GPT-4o mini
To analyze the slope of the line represented by the coordinates \( (0, 24) \) and \( (6, 0) \), we will first find the slope (m) using the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points \( (x_1, y_1) = (0, 24) \) and \( (x_2, y_2) = (6, 0) \):
\[
m = \frac{0 - 24}{6 - 0} = \frac{-24}{6} = -4
\]
The slope of the line is \(-4\).
**Meaning in the Real-World Scenario:**
In the context of the swimmer's race, the slope of \(-4\) indicates that the swimmer is completing 4 laps every minute. This means that for every minute that passes, the number of laps remaining decreases by 4. Therefore, after one minute of swimming, there are 4 laps fewer to complete, and the swimmer will finish the race after 6 minutes, which corresponds to the line going from 24 laps remaining to 0 laps remaining.
So, the correct interpretation is that "**the slope of the line is −4, which means that the swimmer will complete 4 laps every minute.**"
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the given points \( (x_1, y_1) = (0, 24) \) and \( (x_2, y_2) = (6, 0) \):
\[
m = \frac{0 - 24}{6 - 0} = \frac{-24}{6} = -4
\]
The slope of the line is \(-4\).
**Meaning in the Real-World Scenario:**
In the context of the swimmer's race, the slope of \(-4\) indicates that the swimmer is completing 4 laps every minute. This means that for every minute that passes, the number of laps remaining decreases by 4. Therefore, after one minute of swimming, there are 4 laps fewer to complete, and the swimmer will finish the race after 6 minutes, which corresponds to the line going from 24 laps remaining to 0 laps remaining.
So, the correct interpretation is that "**the slope of the line is −4, which means that the swimmer will complete 4 laps every minute.**"