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.
tickets total cost
2 $32:00
3 $44:50
6 $82
What is the equation that models this linear function?
Let x represent the number of tickets and y represent the total cost of the purchase.
We can create the equation by finding the slope (rate of change) and the y-intercept.
From the given data, we can find the slope as the change in y divided by the change in x:
Slope = (total cost change) / (number of tickets change)
Slope = ($44.50 - $32.00) / (3 - 2)
Slope = $12.50 / 1
Slope = $12.50
Next, we can find the y-intercept by substituting one set of values (x, y) into the equation and solving for the y-intercept.
Using the point (2, $32.00):
y = mx + b
$32.00 = $12.50 * 2 + b
$32.00 = $25.00 + b
b = $32.00 - $25.00
b = $7.00
Therefore, the equation that models the linear function is:
y = $12.50x + $7.00
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.
The total cost is a function of the number of tickets, represented by the equation:
Total Cost = $12.50 * Number of Tickets + $7.00
How much is each movie ticket?
To determine the cost of each movie ticket, we need to refer to the equation that models the linear function:
Total Cost = $12.50 * Number of Tickets + $7.00
Since we know that the total cost for purchasing 2 tickets is $32.00, we can substitute this value into the equation:
$32.00 = $12.50 * 2 + $7.00
Now we can solve for the cost of each movie ticket:
$32.00 = $25.00 + $7.00
$32.00 = $32.00
Therefore, each movie ticket costs $12.50.