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Question

A ski club is going to rent a bus for a day trip to the mountains. The rental company will charge an initial booking fee and an additional cost per hour the club rents the bus.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?

Answer 1

In the context of the ski club renting a bus, the linear relationship can be represented by the equation \( y = mx + b \), where:

• \( y \) is the total cost of renting the bus.
• \( m \) is the variable cost (the cost per hour of renting the bus).
• \( x \) is the number of hours the bus is rented.
• \( b \) is the y-intercept.

The y-intercept (\( b \)) represents the initial booking fee charged by the rental company. This means that even if the ski club does not rent the bus for any hours (in other words, if \( x = 0 \)), they would still be charged this initial fee. Therefore, the y-intercept indicates the fixed cost associated with renting the bus, regardless of how long the bus is rented for.