A bowling alley charges $15 per game. Customers are also charged an additional $3 to rent bowling shoes

Which statement is true, based on the given description?

A. The description shows a linear relationship, but not a proportional relationship
B. The description shows a linear relationship and a proportional relationship
C. The description does not show a linear relationship or a proportional relationship

1 answer

To determine the nature of the relationship described in the bowling alley's pricing, let's analyze the charges:

  • The cost per game is $15.
  • There is an additional charge of $3 for renting shoes.

In this case, if we let \( x \) represent the number of games played, the total cost \( C \) can be expressed as:

\[ C = 15x + 3 \]

This equation is linear because it can be represented in the form \( C = mx + b \), where \( m \) is the slope (cost per game) and \( b \) is the y-intercept (the fixed cost of shoe rental).

Now, to determine if it's a proportional relationship, we need to check if the equation passes through the origin (0,0). A proportional relationship would mean that when there are no games played (0 games), the cost should also be $0. However, since the shoe rental adds a fixed cost of $3, when \( x = 0 \), \( C \) would be $3, not $0. Thus, it does not satisfy the condition for a proportional relationship.

Therefore, the correct statement is:

A. The description shows a linear relationship, but not a proportional relationship.