Question

Devin is watering his neighbors' plants while they are on vacation. Each day, he uses a watering can to tend to the potted plants, and then he runs the sprinkler to water the gardens.
There is a linear relationship between the time, in minutes, Devin runs the sprinkler, and the amount of water he uses, in gallons.
the main points are (10,200) (50,900)
Describe the rate of change for this relationship.
The amount of water Devin uses increases by ___ per minute he runs the sprinkler.

Answer 1

To determine the rate of change for the relationship between the time Devin runs the sprinkler (in minutes) and the amount of water he uses (in gallons), we can use the two points given: (10, 200) and (50, 900).

The rate of change (slope) can be calculated using the formula:

\[
\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Where:
- \((x_1, y_1) = (10, 200)\)
- \((x_2, y_2) = (50, 900)\)

Now, substituting the values:

\[
y_2 = 900, \quad y_1 = 200, \quad x_2 = 50, \quad x_1 = 10
\]

Calculating the slope:

\[
\text{Rate of change} = \frac{900 - 200}{50 - 10} = \frac{700}{40} = 17.5
\]

Thus, the amount of water Devin uses increases by **17.5 gallons per minute** he runs the sprinkler.