Let's go through the problem:

Problem Information:

• A swimming pool is draining at a constant rate.
• The table shows the relationship between the number of hours the pool has drained and the change in the water level (in inches).

The given table:

Part a: Find the rate at which the water level is changing per hour.

The water level is changing at a constant rate, so we can calculate the rate (slope) by using the given data. The rate can be found by taking two data points and applying the formula for the slope:

$\text{Rate} = \frac{\Delta y}{\Delta x} = \frac{\text{Change in water level}}{\text{Change in time (hours)}}$

Using the points (2, -3.5) and (17, -29.75):

$\text{Rate} = \frac{-29.75 - (-3.5)}{17 - 2} = \frac{-29.75 + 3.5}{15} = \frac{-26.25}{15} = -1.75 \, \text{inches per hour}$

So, the water level is decreasing at a rate of 1.75 inches per hour.

Part b: Find the change in the water level after 9 hours.

Now that we know the rate is -1.75 inches per hour, we can calculate the change in water level after 9 hours:

$\text{Change} = \text{Rate} \times \text{Time} = -1.75 \times 9 = -15.75 \, \text{inches}$

Thus, after 9 hours, the water level has changed by -15.75 inches.

Part c: Find the change in the water level after 23 hours.

Similarly, after 23 hours:

$\text{Change} = -1.75 \times 23 = -40.25 \, \text{inches}$

So, the water level after 23 hours has changed by -40.25 inches.

Do you need further details or have any questions? Here are 5 related questions to consider:

1. How would you calculate the total amount of water drained if you knew the pool's surface area?
2. What is the meaning of a negative rate in this context?
3. Can you predict how long it will take for the pool to be completely empty if it continues draining at this rate?
4. If the pool’s water level started at 0 inches, what would the water level be after 30 hours?
5. How would you model this situation with an equation that predicts the water level based on time?

Tip: Always double-check units to ensure your rate matches the units given in the problem.