Final answer:
To find the equation for the relationship between the number of tickets and the total cost, we need to determine the pattern or trend in the given data points. The equation for the relationship is y = 27x, where y represents the total cost and x represents the number of tickets.
Step-by-step explanation:
To find the equation for the relationship between the number of tickets and the total cost, we need to determine the pattern or trend in the given data points. Looking at the given data, we can see that the total cost is increasing by 27 for every additional ticket. This means that the tickets have a constant rate of change. We can represent this relationship with a linear equation of the form y = mx + b, where y represents the total cost, x represents the number of tickets, m represents the slope, and b represents the y-intercept.
From the data points, we can calculate the slope:
m = (change in total cost) / (change in number of tickets)
m = (81 - 54) / (3 - 2)
m = 27
Substituting the slope and one set of data points (e.g. 2 tickets and 54 total cost) into the equation, we can solve for the y-intercept (b):
54 = 27(2) + b
54 = 54 + b
b = 0
Therefore, the equation for the relationship is y = 27x, where y represents the total cost and x represents the number of tickets.