Question

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? 6. higher order thinking the table and graph show the costs to buy dvds at two different stores. a. which store has the better deal on dvds? explain. b. how much money will sheila save if she buys 20 dvds at the store with the better deal than at the other store? assessment practice 7. does the graph at the right show a proportional relationship between x and y? explain. 8. the graph at the right shows the relationship between the weight of silver and the total cost. which of the following statements about the graph are true? the point (0, 0) means that 0 pounds of silver cost $0.00. the point (1, 17) shows the constant of proportionality. the point (4, 68) means that $4.00 is the cost for 68 pounds of silver. the point (2, 34) means that 34 pounds of silver cost $2.00 per pound. the graph shows a proportional relationship.

Explanation:

Step1: Calculate the unit price for Store A

For Store A, when \(x = 2\), \(y=6.30\). The unit price \(k_A=\frac{y}{x}=\frac{6.30}{2}=3.15\). When \(x = 3\), \(y = 9.45\), \(k_A=\frac{9.45}{3}=3.15\). When \(x = 4\), \(y=12.60\), \(k_A=\frac{12.60}{4}=3.15\).

Step2: Calculate the unit price for Store B

From the graph of Store B, when \(x = 2\), \(y = 6.40\). The unit price \(k_B=\frac{y}{x}=\frac{6.40}{2}=3.2\)

Step3: Compare the unit prices

Since \(k_A = 3.15

Step4: Calculate the cost for 20 DVDs in Store A

The cost \(y_A\) for \(x = 20\) DVDs in Store A is \(y_A=k_A\times x=3.15\times20 = 63\)

Step5: Calculate the cost for 20 DVDs in Store B

The cost \(y_B\) for \(x = 20\) DVDs in Store B is \(y_B=k_B\times x=3.2\times20=64\)

Step6: Calculate the savings

The savings \(S=y_B - y_A=64 - 63=1\)

Answer:

a. Store A has the better deal. Because the unit - price of DVDs in Store A (\(3.15\) per DVD) is less than that in Store B (\(3.2\) per DVD).
b. Sheila will save \(1\) dollar.