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.
What is the equation that models this linear function?
To determine the equation that models this linear function, we need to examine the relationship between the number of tickets and the total cost of the purchase. From the given table, we can see that as the number of tickets increases, the total cost also increases.
Let's denote the number of tickets as x and the total cost as y. We can see that the total cost is a linear function of the number of tickets. Therefore, the equation that models this linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
From the table, we can determine that when x = 0, the y-intercept is $1.50. This means that even if Vinh reserves zero tickets, he still has to pay a convenience fee of $1.50.
Next, we need to calculate the slope. We can pick any two points from the table to determine the slope. Let's select the points (2, $6.00) and (4, $10.50).
The slope (m) is calculated as:
m = (change in y) / (change in x)
m = ($10.50 - $6.00) / (4 - 2)
m = $4.50 / 2
m = $2.25
Now with the slope (m = $2.25) and the y-intercept (b = $1.50), we can write the equation:
y = 2.25x + 1.50
Therefore, the equation that models this linear function is y = 2.25x + 1.50.