Final answer:
A and D indicate a proportional relationship between x (time) and y (distance), with A showing a direct equation and D suggesting a constant rate; B may suggest proportionality but lacks sufficient detail to confirm it.
Step-by-step explanation:
To determine if x and y have a proportional relationship, we should look for consistency in the ratio of y to x. Specifically, this means that y is directly proportional to x, and can be modeled by an equation of the form y = kx, where k is the constant of proportionality.
Let's examine the options:
- A. y=3x suggests a direct proportion between y and x because as x changes, y changes by 3 times that amount consistently.
- B. After 4 minutes, the turtle has walked 12 feet away from the rock. To determine if this is proportional, we need to know if this rate continues consistently over time.
- C. The turtle walks for a bit, then stops for a minute before walking again. This describes inconsistent behavior that does not necessarily indicate a proportional relationship as stopping would affect the ratio of distance to time.
- D. The turtle walks away from the rock at a constant rate. This indicates a proportional relationship because a constant rate means that the distance covered (y) and the time taken (x) would change in direct proportion to each other.
Based on this information, options A and D suggest that x and y have a proportional relationship because they indicate a direct and constant ratio between distance and time. Option B could also suggest a proportional relationship if the rate remains constant, but we need additional information to confirm this.