Question

1. the graph below represents the total cost of admission to an amusement park based on the number of tickets purchased.

graph of amusement park with total cost on y - axis (from -16 to 128) and number of tickets on x - axis (from 0 to 18), with points plotted at (4, 32), (8, 64), (12, 96), (16, 128)

which of the following statements best represents the data in the graph?

a. the graph is non - linear because the graph shows only four points.

b. the number of tickets depends on the total cost of the tickets.

c. the unit rate is $4 for 1 ticket.

d. the graph is proportional because the line containing the four points passes through the origin.

Explanation:

Step1: Analyze Option A

A graph's linearity isn't determined by the number of points. A linear relationship has a constant rate of change. So A is incorrect.

Step2: Analyze Option B

In the context, total cost depends on the number of tickets (not the other way). So B is incorrect.

Step3: Analyze Option C

Check the points: At 4 tickets, cost is 32. Unit rate = \( \frac{32}{4} = 8 \), not 4. So C is incorrect.

Step4: Analyze Option D

A proportional relationship has a linear graph passing through the origin. Let's check the line through the points. The points seem to lie on a line that would pass through (0,0) (since when tickets=0, cost=0 is implied for proportionality), and the relationship is linear (constant rate). So D is correct.

Answer:

D. The graph is proportional because the line containing the four points passes through the origin.