Question

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

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**.