The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.

Question

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 30 to 10 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 negative one third, which means that the swimmer completes a lap in one third of a minute.
The slope of the line is −3, which means that the swimmer will complete 3 laps every minute.
The slope of the line is 10, which means that the swimmer will finish the race after 10 minutes.
The slope of the line is 30, which means that the swimmer must complete 30 laps in the race.

Answer 1

To determine the correct interpretation of the slope from the graph described, let's break down the given points and their meanings.

From the information provided, we have two points on the line:

• (0, 30) which indicates that at 0 minutes, there are 30 laps remaining.
• (10, 0) which indicates that at 10 minutes, the swimmer has completed all laps (0 laps remaining).

Now, we can calculate the slope (m) of the line using the formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In our case, we will use the points (0, 30) and (10, 0): \[ m = \frac{0 - 30}{10 - 0} = \frac{-30}{10} = -3 \]

So, the slope of the line is \(-3\).

Interpretation of the Slope

The negative slope of -3 indicates that the swimmer is completing 3 laps every minute. Specifically, for every 1 minute that passes, the number of laps remaining decreases by 3.

This means that the swimmer is quite efficient and finishes 3 laps in just 1 minute. Therefore, this interpretation is accurately captured in the option:

The slope of the line is −3, which means that the swimmer will complete 3 laps every minute.