The problem describes a situation where a swimming pool is being drained at a constant rate of 15 gallons per minute. Initially, the pool holds 1,200 gallons of water. To find the equation that represents the amount of water, $g$, left in the pool after $t$ minutes, we can set up a linear relationship.

1. The pool starts with 1,200 gallons, and every minute, 15 gallons are drained.
2. Therefore, the amount of water in the pool decreases by 15 gallons for every minute that passes.

This gives us the equation: $g = 1200 - 15t$ Rearranging it, we see that it matches the form of option C: $g = -15t + 1200$

Correct Answer: C. g = -15t + 1,200

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the pool was being filled at 15 gallons per minute instead of drained?
2. What would the equation be if the initial volume of the pool was different, say 2,000 gallons?
3. How much water would be left in the pool after 30 minutes of draining?
4. How long will it take for the pool to completely empty?
5. What would happen to the slope of the equation if the draining rate increased to 20 gallons per minute?

Tip: The slope in a linear equation often represents the rate of change in problems involving time and quantity, such as draining or filling.