Question

suppose you were to create a scatter plot of the data for speed and distance traveled. would you expect to see a positive, negative, or no relationship between the two variables. explain your answer.
a. negative relationship; as the speed decreases, the distance increases.
b. positive relationship; as the speed decreases, the distance increases.
c. positive relationship; as the speed increases, the distance increases.
d. no relationship.

please select the best answer from the choices provided

○ a
○ b
○ c
○ d

Explanation:

To determine the relationship between speed and distance traveled, we use the formula \( d = vt \) (distance = speed × time). Assuming time is constant (or at least, as speed increases, with time considered, distance should increase if time is non - negative). A positive relationship means that as one variable increases, the other also increases.

• Option A: Says negative relationship with wrong reasoning (speed decrease and distance increase is wrong as per \( d = vt \)).
• Option B: Wrong reasoning (speed decrease and distance increase is incorrect).
• Option C: Correct. As speed (\( v \)) increases, for a given time (or in general, when time is a non - negative quantity), distance (\( d=vt \)) will increase. So there is a positive relationship.
• Option D: Incorrect as we know from the formula that speed and distance (with time considered) are related.

Answer:

C. positive relationship; as the speed increases, the distance increases.