Which one of the following scenarios can be modeled by a linear function?

Question

The total distance traveled by a delivery truck if the speed varies based on traffic.
The total distance traveled by a delivery truck if the speed varies based on traffic.

The total distance traveled by a biker if the biker rides a different number of miles each day.
The total distance traveled by a biker if the biker rides a different number of miles each day.

The total cost of a bag of groceries if the bag contains many different items.
The total cost of a bag of groceries if the bag contains many different items.

The total cost of building a new home if the builder charges $300 per square foot.

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.

This situation represents a linear relationship because the total cost is directly proportional to the number of square feet. If \( x \) is the number of square feet, the total cost \( C \) can be expressed as:

\[ C = 300x \]

where \( 300 \) is the constant rate charged per square foot. All other scenarios involve variables that do not provide a consistent linear relationship.