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Difficulty: EasyInterpreting Linear Relationships in Context

A moving company uses the equation C=2.5d+75C = 2.5d + 75 to determine the total charge CC, in dollars, for renting a small truck and driving it dd miles. According to the relationship, what is the charge, in dollars, for each mile the truck is driven?

Answer: 2.5 dollars

Answer

The charge for each mile the truck is driven is 2.5 dollars.
In the linear model C=2.5d+75C = 2.5d + 75, the total cost CC is a function of the number of miles driven dd. The rate of change of this function represents the cost per mile driven. In the equation, this rate of change is the coefficient of dd, which is 2.5. Therefore, the charge for each mile the truck is driven is 2.5 dollars.

Step-by-Step Solution

1
Analyze the linear equation C=2.5d+75C = 2.5d + 75 to determine the relationship between variables.
The total charge CC depends on the number of miles dd driven, with a rate of change of 2.5 dollars per mile and a base fee of 75 dollars.
Understanding the components of a linear equation helps isolate the rate of change.
2
Identify the coefficient of the independent variable dd.
The coefficient of dd is 2.5.
In a linear equation of the form y=mx+by = mx + b, the coefficient of the independent variable represents the rate of change.
3
Interpret the meaning of this coefficient in the context of the problem.
The coefficient 2.5 represents the cost, in dollars, incurred per mile driven.
The question asks for the charge per mile, which corresponds to the rate of change.

Key Concept

Interpreting Linear Relationships in Context
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Topics

Interpreting Linear Relationships in Context

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