Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase for different number of tickets in the table shown.

Question

What is the equation that models this linear function? Show your work. Don’t forget to define your variables!

Use the phrase is a function of to describe the situation Tickets 2 3 6 Total Cost $32.00 $44.50 $82.00 represented by the equation you wrote in problem 3a.

How much is each movie ticket?

Answer 1

Let x be the number of tickets and y be the total cost.

From the given table, we can observe that Vinh pays $32.00 for 2 tickets, $44.50 for 3 tickets, and $82.00 for 6 tickets.

We can see that the cost increases by $12.25 for each additional ticket.

Therefore, the equation that models this linear function is y = 12.25x + b, where b represents the base cost.

To find the value of b, we can substitute the values of x and y from any point on the table into the equation. Let's use the first point, x = 2 and y = 32.00:

32.00 = 12.25(2) + b
32.00 = 24.50 + b
b = 32.00 - 24.50
b = 7.50

Therefore, the equation becomes y = 12.25x + 7.50.

The phrase "is a function of" in this situation would be "Total Cost is a function of the number of tickets."

To find the cost of each movie ticket, we can rearrange the equation:

y = 12.25x + 7.50
Total cost = Cost per ticket * Number of tickets + Base cost

Comparing this to the given table, we can see that the base cost is $7.50.

Therefore, each movie ticket costs $7.50.