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Question

Mathematics
Expert-Verified
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.

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Answer 1

To determine the rate at which the depth of the water in the pond is changing, we can calculate the slope of the line formed by the points (2, 4) and (4, 8).

The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Plugging in the values from the points:

• \( (x_1, y_1) = (2, 4) \) and \( (x_2, y_2) = (4, 8) \)

We have:

\[ m = \frac{8 - 4}{4 - 2} = \frac{4}{2} = 2 \]

This means the depth of the water is increasing by 2 feet each minute.