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?

The Table:
Tickets: Total Cost:
2 32.00
3 44.00
6 82.00

Answer 1

Let's define the variables:
Let "x" represent the number of tickets.
Let "y" represent the total cost.

From the table, we can see that when Vinh buys 2 tickets, the total cost is $32.00. This gives us the coordinate (2, 32).
Similarly, when Vinh buys 3 tickets, the total cost is $44.50. This gives us the coordinate (3, 44.50).
Finally, when Vinh buys 6 tickets, the total cost is $82.00. This gives us the coordinate (6, 82).

To find the equation that models this linear function, we can use the slope-intercept form of a linear equation, y = mx + b, and substitute the coordinates to find the values of "m" and "b."

First, we need to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (44.50 - 32.00) / (3 - 2)
m = 12.50 / 1
m = 12.50

Now we have the slope, let's use the point-slope form of a linear equation, y - y1 = m(x - x1), and substitute one of the coordinates:

Using the coordinate (3, 44.50):
y - 44.50 = 12.50(x - 3)
y - 44.50 = 12.50x - 37.50
y = 12.50x - 37.50 + 44.50
y = 12.50x + 7

So, the equation that models this linear function is:
y = 12.50x + 7

According to the equation, the total cost (y) is a function of the number of tickets (x).

To find the cost of each movie ticket, we can substitute the value of "x" with any number of tickets in the equation.
Let's use the coordinate (2, 32) to find the cost of each movie ticket:
32 = 12.50(2) + 7
32 = 25 + 7
32 = 32

Each movie ticket costs $12.50.