Question

the water level in a tub is changing at a constant rate. the table shows the relationship between the time in minutes, x, and the height of the water in liters, y. determine the rate of change of the water level with respect to time. then, interpret the rate of change in terms of the problem situation. move the correct at box. not all answers will be used. the rate of change of the water level with respect to time is. this means the amount of water in the tub is at a rate of liters per minute.

Explanation:

Step1: Calculate the rate of change

The formula for the rate of change (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(0,360)\) and \((x_2,y_2)=(2,240)\).
\(m=\frac{240 - 360}{2-0}=\frac{- 120}{2}=-60\)

Step2: Interpret the rate of change

Since the rate of change \(m=-60\), the negative sign indicates that the amount of water is decreasing. The magnitude \(|m| = 60\) means the amount of water changes by 60 liters per minute.

Answer:

The rate of change of the water level with respect to time is \(-60\). This means the amount of water in the tub is \(decreasing\) at a rate of \(60\) liters per minute.