Question

Jonathan is making a graph that shows the proportional relationship between the amount of money collected, y, and the number of tickets sold, x. He correctly plots the point (75, 600). Which of these statements are true? Choose all that apply.

A. The equation is y = 8x.
B. The point (5, 40) is not a point on the graph.
C. The constant of proportionality is 600/75, which is equal to 8.5.
D. The point (1, 0.5) is on the graph and identifies that the cost for each ticket is $0.50.
E. The point (10, 80) is on the graph because $10 will be collected if 80 tickets are sold.

Answer 1

Two statements about Jonathan's proportional relationship graph are true: the equation is y = 8x (point 75, 600 confirms this) and the point (10, 80) lies on the graph. Points (5, 40), (1, 0.5), and the constant of proportionality being 600/75 = 8.5 are incorrect.

Step-by-step explanation:

Let's examine the provided information about Jonathan's graph of the proportional relationship between the amount of money collected, y, and the number of tickets sold, x. We are given that the point (75, 600) lies on the graph. This means that for every ticket sold, the amount of money collected can be figured out by the ratio 600/75, which simplifies to 8. Hence, the correct equation describing the proportional relationship is y = 8x.

• The equation is y = 8x. (True).
• The point (5, 40) is indeed on the graph since 40 equals 5 multiplied by 8.
• The constant of proportionality is 600/75, which is equal to 8, not 8.5. (False).
• The point (1, 0.5) is not on the graph because according to the equation y = 8x, if x equals 1, y should be 8, not 0.5. This point also does not identify the cost of each ticket since the calculation is incorrect. (False).
• The point (10, 80) is on the graph because 10 times 8 is indeed 80; this statement is interpreted correctly based on the equation. (True).

Therefore, the statements A and E are true, while B, C, and D are false.