Question

The following graph shows the relationship between the number of times a gear can rotate in a period of time. Which of the following statements is true?

A) If the gear rotates 30 times, then it has been rotating for 1.5 minutes.
B) The graph satisfies the equation y = 10x.
C) The relationship is non-proportional.
D) Explain which statement accurately describes the information presented in the graph.

Answer 1

The graph shows a non-proportional relationship between the number of times a gear can rotate and the time it takes. Statement C, which states that the relationship is non-proportional, accurately describes the information presented in the graph.

Step-by-step explanation:

The graph shows the relationship between the number of times a gear can rotate and the time it takes for the rotations. Let's analyze each statement:

1. Statement A: If the gear rotates 30 times, we can see that it takes 5 seconds on the graph. Since 1 minute has 60 seconds, we can calculate the time it takes for 30 rotations as follows: 5 seconds × (1 minute / 60 seconds) = 0.0833 minutes. Therefore, Statement A is incorrect.
2. Statement B: The equation y = 10x corresponds to a linear relationship, where y (the number of rotations) is directly proportional to x (the time). Looking at the graph, this is not the case since the line is curving. Therefore, Statement B is incorrect.
3. Statement C: Since the graph is not a straight line and the rate of change is not constant, the relationship is non-proportional. Therefore, Statement C is correct.

Based on the analysis above, the accurate statement that describes the information presented in the graph is Statement C, which states that the relationship is non-proportional.