CARS Car model A costs 22,000 to purchase and .12 per mile...

CARS Car model A costs $\$ 22,000$ to purchase and $\$ .12$ per mile to maintain. Car model B costs $\$ 24,500$ to purchase and $\$ .10$ per mile to maintain.
Use the graph to determine how many miles each car must be driven for the total costs of the two models to be the same.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fixed and Variable Costs

This concept involves separating the total cost into two components: a fixed cost that does not change with usage (such as a purchase price) and a variable cost that depends on the level of activity (such as cost per mile). Understanding these allows for a clear formulation of cost models for various scenarios.

Linear Functions

A linear function models a straight-line relationship between two quantities, typically expressed in the form y = mx + b, where m represents the rate of change and b is the initial value. This framework simplifies the analysis of scenarios where one quantity changes at a constant rate with respect to another.

Equating Linear Cost Functions

Equating two linear functions is a method to find the point where the costs or outputs of two different models become equal. By setting the two expressions equal to each other, one can solve for the variable of interest, such as the number of miles driven in cost comparisons.

Graphical Interpretation of Linear Equations

Graphing linear equations provides a visual representation of the relationship between variables, with the intersection point of two lines indicating the solution to the equations when they are set equal. This approach aids in understanding how different costs accumulate and when they become identical.

Transcript

Please give Ace some feedback