The graph shows the rate at which the depth of the water in a pond is changing over time.

Question

On a coordinate plane, a graph titled Depth of Pond Water has Minutes on the x-axis and Feet on the y-axis. A line goes through points (2, 4) and (4, 8).

The depth of the water is increasing by feet each minute.

Answer 1

To determine how much the depth of the water is increasing each minute, we can analyze the two points provided: (2, 4) and (4, 8).

1. Identify the coordinates:

   • At 2 minutes, the depth is 4 feet.
   • At 4 minutes, the depth is 8 feet.

2. Calculate the change in depth: \[ \text{Change in depth} = \text{Depth at } (4,8) - \text{Depth at } (2,4) = 8 - 4 = 4 \text{ feet} \]

3. Calculate the change in time: \[ \text{Change in time} = 4 \text{ minutes} - 2 \text{ minutes} = 2 \text{ minutes} \]

4. Determine the rate of change: \[ \text{Rate of change} = \frac{\text{Change in depth}}{\text{Change in time}} = \frac{4 \text{ feet}}{2 \text{ minutes}} = 2 \text{ feet per minute} \]

Therefore, the depth of the water is increasing by 2 feet each minute.