Question

needs to empty the seahorse tank for cleaning. the gallons of water in the tank based on the number of minutes it has been draining is shown in the table below.

minutes | gallons
0 | 60
4 | 50
8 | 40
12 | 30

statement | t/f?
the situation can be represented by the equation $y = 2.5x + 60$.
the aquarium initially contained 60 gallons of water.
the aquarium drains at a rate of 2.5 gallons per minute.

rewrite the false statement to make it true:

Explanation:

Step1: Check initial water amount

At $x=0$ minutes, $y=60$ gallons.

Step2: Calculate drain rate

Rate = $\frac{\text{Change in gallons}}{\text{Change in minutes}} = \frac{60-50}{4-0} = 2.5$ gallons per minute (decreasing, so negative slope).

Step3: Verify the equation

The correct linear equation for draining is $y = -2.5x + 60$, not $y=2.5x+60$.

Step4: Evaluate each statement

1. Equation $y=2.5x+60$: False (slope should be negative).
2. Initial 60 gallons: True (matches $x=0$ value).
3. Drain rate 2.5 gal/min: True (calculated rate matches).

Answer:

1. The situation can be represented by the equation $y = 2.5x + 60.$: False
2. The aquarium initially contained 60 gallons of water.: True
3. The aquarium drains at a rate of 2.5 gallons per minute.: True

Rewritten true statement: The situation can be represented by the equation $y = -2.5x + 60$.