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Difficulty: EasyInterpreting Linear Relationships in Context

A landscaping service uses a water tank to irrigate lawns. The volume of water, VV, in gallons, remaining in the tank after nn lawns have been irrigated is modeled by the equation V=850−25nV = 850 - 25n. According to the model, by how many gallons does the volume of water in the tank decrease for each lawn that is irrigated?

Answer: 25 gallons

Answer

The correct answer is 25, which represents the decrease in the volume of water in the tank, in gallons, for each lawn irrigated.
In the linear equation V=850−25nV = 850 - 25n, the coefficient of nn is −25-25. This coefficient represents the rate of change of the volume of water with respect to the number of lawns irrigated. The negative sign shows that the volume is decreasing, and the magnitude, 25, indicates that the volume decreases by 25 gallons for each lawn irrigated.

Step-by-Step Solution

1
Identify the coefficient of the variable nn in the equation V=850−25nV = 850 - 25n.
The coefficient of nn is −25-25.
The coefficient of the independent variable in a linear equation represents the rate of change of the dependent variable.
2
Interpret the coefficient in terms of the real-world context.
The coefficient −25-25 means the volume of water decreases by 25 gallons for each lawn irrigated.
The negative sign indicates a decrease, and the magnitude represents the amount of change per unit.

Key Concept

Interpreting the slope of a linear relationship in context.
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Topics

Interpreting Linear Relationships in Context

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