The image shows a graph depicting a diver's net change in depth $y$ in feet over a number of seconds $x$. The graph appears to represent a linear relationship between time and depth, and the question asks which of the provided statements about the diver's descent rate is true.

Let's break down the situation:

1. The graph shows that as time increases, the diver's depth (in feet) decreases. The line is sloping downward, which means the diver is descending.
2. From the graph, it seems that the diver starts at 0 seconds and descends to -12 feet after 8 seconds.

To calculate the diver's descent rate:

• The rate of descent can be found by determining the slope of the line, which represents the rate of change in depth per second.
• Slope $m$ is calculated by the formula: $m = \frac{\Delta y}{\Delta x}$ where $\Delta y$ is the change in depth (feet) and $\Delta x$ is the change in time (seconds).

In this case:

• The change in depth $\Delta y$ is from 0 feet to -12 feet, so $\Delta y = -12$.
• The change in time $\Delta x$ is from 0 seconds to 8 seconds, so $\Delta x = 8$.

Thus, the rate of descent is: $m = \frac{-12}{8} = -\frac{3}{2}$ This means the diver descends $\frac{3}{2}$ feet, or 1.5 feet, per second.

Now, let's analyze the answer choices:

• A. The diver descends $\frac{3}{2}$ feet in 1 second.
  This is correct since we calculated that the diver descends 1.5 feet per second.
• B. The diver descends 4 feet in 1 second.
  This is incorrect because the rate is 1.5 feet per second.
• C. The diver descends 8 feet in 1 second.
  This is incorrect for the same reason.
• D. The diver descends $\frac{1}{3}$ feet in 1 second.
  This is also incorrect.

Correct Answer: A – The diver descends $\frac{3}{2}$ feet in 1 second.

Would you like more details on any part of this solution?

Here are 5 related questions you might find helpful:

1. How is the slope of a line related to rate of change in real-world scenarios?
2. What are other real-life examples where we use slope to determine rates?
3. How would the graph look if the diver ascended instead of descended?
4. What if the diver descended faster – how would that affect the slope?
5. How can you calculate the total depth after any given time?

Tip: To determine a linear rate of change, always think of slope as "rise over run" — how much the vertical value (depth) changes for every unit of horizontal value (time).