Final answer:
The linear equation for the Ghost Tour company's fee structure is y = 25 + 15x, with a y-intercept of $25 and a slope of $15. However, the equation is not proportional since it includes a one-time membership fee and does not pass through the origin.
Step-by-step explanation:
Understanding the Linear Relationship in Costs
The scenario provided involves a Ghost Tour company creating a club for ghost hunters, where there is a one-time fee and a monthly charge to participate in ghost tours. This cost structure can be modeled by a linear equation, similar to how Svetlana's tutoring and other service charges work. In this case, the y-intercept of the Ghost Tour company's cost function is $25, which represents the initial, one-time fee a person must pay to join the club. This occurs when the number of months (x) is zero.
The slope of the line is $15, indicating that for each additional month of membership, a person must pay an additional $15. This rate of change in cost per month tells us how the total cost increases with each passing month.
An equation representing this situation would be y = 25 + 15x, where y represents the total cost after x months of membership. Since there is a one-time fee, the equation is not proportional as it does not pass through the origin. Proportional relationships must have a y-intercept of zero; they start at the origin (0,0) and have a constant rate of change, unlike the Ghost Tour company's fee structure.