Question

a bathtub that contains 20 gallons of water drains at a steady rate. the graph shows the amount of water in the tub, $y$, as a function of the number of minutes the tub drains, $x$.
use the graph to describe the function.
the initial value is 20 .
it represents the amount of water in the tub before it starts to drain .
the $y$-values decrease as the $x$-values increase, so the function has a negative rate of change.
the amount of water decreases by ? gallons each minute the tub drains.
the rate of change is ? .

Explanation:

Step1: Identify total change in water

Total water lost: $20 - 0 = 20$ gallons

Step2: Identify total time to drain

Total time: $4 - 0 = 4$ minutes

Step3: Calculate per-minute decrease

Divide total loss by time: $\frac{20}{4} = 5$

Step4: Find rate of change

Rate of change = $\frac{\Delta y}{\Delta x} = \frac{0-20}{4-0} = -5$

Answer:

The amount of water decreases by 5 gallons each minute the tub drains.
The rate of change is -5.