Question

Penelope is moving and must rent a truck. There is an initial charge for the rental plus a fee per mile driven. Let cc represent the total cost of renting the truck when the truck is driven mm miles. A graph of cc is shown below. Write an equation for cc, then state the yy-intercept of the graph and determine its interpretation in the context of the problem.

Answer 1

The cost equation for renting a truck is of the format c = pm + f, where p is the fee per mile, and f is the initial rental charge represented by the y-intercept, which signifies the cost of renting the truck before mileage is added.

Step-by-step explanation:

The question asks for the formulation of an equation for the cost c of renting a truck based on the number of miles m driven, as well as an interpretation of the y-intercept of the graph representing this relationship. In a similar situation described in the reference material, an auto mechanic charges a flat fee plus an hourly rate for labor costs, represented by an equation of the form y = mx + b, where m is the slope (rate per hour) and b is the y-intercept (the flat fee).

Similarly, for Penelope's truck rental situation, the equation would be of the form c = pm + f, where p is the fee per mile (slope of the graph) and f is the initial charge (y-intercept). The y-intercept in this context represents the cost of renting the truck before any miles are driven. For instance, if the graph showed a y-intercept of $50, it would mean Penelope has to pay $50 just to rent the truck, regardless of the distance driven.