Cost of Driving a Car The annual fixed costs for owning a...

Cost of Driving a Car The annual fixed costs for owning a small sedan are $$\$ 6735,$$ assuming the car is completely paid for. The cost to drive the car is approximately $$\$ 0.45$$ per mile. Write a linear equation that relates the cost $C$ and the number $x$ of miles driven annually. Source: $A A A,$ April 2012

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Key Concepts

Linear Equation

A linear equation is an expression of the relationship between two variables where the change in one variable is proportional to the change in the other. In this context, it models the total cost as a function of the distance driven using a straight-line relationship.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope, indicating the rate of change, and b is the y-intercept, representing the fixed cost when the independent variable is zero. This form is used to combine fixed and variable costs into one equation.

Fixed Costs

Fixed costs are expenses that do not change with the number of miles driven. They remain constant regardless of the vehicle usage, such as insurance, registration fees, or in this case, the annual cost of owning the car when it is already paid off.

Variable Costs

Variable costs change in direct proportion to the number of miles driven. They represent the cost incurred per unit of activity (mileage), such as fuel costs, maintenance, or any charges that accumulate with increased driving.

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