To model the diver's elevation over time, we start by defining the initial position and the rate of descent:

1. The diver begins 30 feet below sea level, which is represented as an initial position of $-30$ feet.
2. The diver descends at a rate of 5 feet per minute. Since the diver is descending, this rate will be represented as a negative value, $-5$.

Let $y$ represent the diver's elevation after $x$ minutes. We can write the equation for the diver’s elevation as follows:

$y = -30 - 5x$

Explanation:

• $-30$ represents the initial elevation (30 feet below sea level).
• $-5x$ represents the decrease in elevation over time, with $x$ being the number of minutes.

Thus, the equation that represents the diver's elevation $y$ after $x$ minutes is:

$y = -30 - 5x$

Do you want details on any part of this problem? Let me know if you have any questions.

Related Questions:

1. If the diver started at a different depth, say 20 feet below sea level, how would the equation change?
2. How would the equation change if the diver ascended instead of descended?
3. After how many minutes will the diver be 60 feet below sea level?
4. If the diver descends for 10 minutes, what will their elevation be?
5. How would the equation change if the rate of descent was 7 feet per minute?

Tip:

Always pay attention to signs when working with elevations and rates. Negative values typically represent positions or movements below a reference point, like sea level in this case.