Question

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1. two tickets to an ice skating performance costs $36. for five tickets it costs $90, and for nine tickets it costs $162. model with math use the graph to determine whether the number of tickets and the cost have a proportional relationship. if so, what is the constant of proportionality and what does it mean?

Explanation:

Step1: Calculate the unit rate for each pair

For \(2\) tickets costing \(\$36\), the unit rate \(r_1=\frac{36}{2}=18\).
For \(5\) tickets costing \(\$90\), the unit rate \(r_2 = \frac{90}{5}=18\).
For \(9\) tickets costing \(\$162\), the unit rate \(r_3=\frac{162}{9}=18\).

Step2: Check proportionality

Since \(\frac{y}{x}=18\) (constant) for all given pairs \((x,y)\) (where \(x\) is the number of tickets and \(y\) is the cost), the relationship is proportional.

Answer:

The number of tickets and the cost have a proportional relationship. The constant of proportionality is \(18\). It means that each ticket costs \(\$18\).