Question

which one of the following scenarios can be modeled by a linear function? (1 point) the total distance traveled by a biker if the biker rides a different number of miles each day. the total distance traveled by a delivery truck if the speed varies based on traffic. 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.

Explanation:

A linear function has a constant rate of change. Let's analyze each option:

• First option: Biker rides different miles daily, so rate (miles per day) isn't constant. Not linear.
• Second option: Truck speed varies with traffic, so rate (distance over time) isn't constant. Not linear.
• Third option: Groceries have different items with different costs, so cost per item isn't constant. Not linear.
• Fourth option: Builder charges $300 per square foot (constant rate). Total cost = 300 × square footage, which is linear (form \( y = mx + b \), here \( b = 0 \), \( m = 300 \)).

Answer:

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