Question

Which one of the following scenarios can be modeled by a linear function the total cost of a bag of groceries if the bag contains many different items the total distance traveled by a biker if the bike rides a different number of miles each day the total cost of building a new home if the builder charges $300 per square foot the total distance traveled by delivery truck if the speed varies based on traffic

Answer 1

The scenario that can be modeled by a linear function is "the total cost of building a new home if the builder charges $300 per square foot."

In this case, the total cost is directly proportional to the area of the home (in square feet), and can be represented by the equation:

\[ \text{Total Cost} = 300 \times \text{Area (in square feet)} \]

This creates a straight line when graphed, indicating a linear relationship.

The other scenarios involve varying factors (like different items in groceries, varying distance in biking, and varying speed in delivery) that do not lend themselves to a consistent linear relationship.