Question 1169601: England. Like everything else, the ticket prices to Six Flags continue to increase every year. Because of this, your family is planning to buy a family membership this year that includes reduced admission costs, discounts on food and drinks, free parking and “skip the line” passes every time you visit.
Your parents have asked you to determine which membership plan would be best for your family. The table below summarizes the three membership options:
O1 Gold membership: $225 per visit
O2 Platinum Membership: Original payment of $750 plus $100 every visit.
O3 Diamond Membership: You pay an initial membership fee of $1575. On your first visit you pay $25, on your second visit you pay $50 and on your third visit you pay $75. This constant rate of change applies to every visit you make.
Let C represent the cost function and let v represent the number of visits to Six Flags you make during the summer months. Write a linear function in slope intercept form for each membership option. Is there a y-intercept for each option? What is the rate of change for each option? Use the variables identified in the word problem to write the equations.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely, let's analyze the Six Flags membership options and create linear functions for each.
**Understanding the Problem**
We need to create linear functions (in slope-intercept form, y = mx + b) for the cost of each membership option based on the number of visits. We also need to identify the y-intercept and the rate of change for each option.
**Variables**
* C: Total cost
* v: Number of visits
**Membership Options**
* **O1 Gold Membership:**
* Cost: $225 per visit
* Equation: C = 225v
* Y-intercept: 0 (no initial fee)
* Rate of change: 225 (cost increases by $225 per visit)
* **O2 Platinum Membership:**
* Cost: $750 initial payment + $100 per visit
* Equation: C = 100v + 750
* Y-intercept: 750 (initial payment of $750)
* Rate of change: 100 (cost increases by $100 per visit)
* **O3 Diamond Membership:**
* Cost: $1575 initial payment + $25 for the first visit, $50 for the second visit, $75 for the third visit, etc.
* This indicates that the cost per visit increases by $25 for each subsequent visit.
* To find the general equation, we need to find the cost per visit for the "v"th visit.
* The cost for the "v"th visit will be 25 * v.
* Therefore the total cost is.
* Equation: C = 1575 + 25v
* Y-intercept: 1575 (initial payment of $1575)
* Rate of change: 25 (cost increases by $25 per visit)
**Summary**
* **O1 Gold:** C = 225v
* Y-intercept: 0
* Rate of change: 225
* **O2 Platinum:** C = 100v + 750
* Y-intercept: 750
* Rate of change: 100
* **O3 Diamond:** C = 25v + 1575
* Y-intercept: 1575
* Rate of change: 25
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