Question

which of the following best describes the relationship between flight length and average speed?
a. the scatterplot has a linear shape and shows a positive relationship between flight length and speed.
b. the scatterplot has a curved shape and shows a positive relationship between flight length and speed.
c. the scatterplot has a linear shape and shows a negative relationship between flight length and speed.
d. the scatterplot has a curved shape and shows a negative relationship between flight length and speed.
(there is a scatterplot with x - axis labeled average speed (mph) and y - axis labeled flight length (miles))

Explanation:

Step1: Analyze Scatterplot Shape

Check if the points form a linear or curved pattern. The scatterplot's points seem to follow a curved (non - linear) trend.

Step2: Analyze Relationship Direction

As average speed (x - axis) increases, flight length (y - axis) generally increases? Wait, no—wait, looking at the axes: x is average speed (mph), y is flight length (miles). Wait, no, wait the labels: "average speed (mph)" on x, "flight length (miles)" on y. Wait, when speed increases, does flight length increase? Wait, no, the points: when speed is lower (left on x), flight length is lower; when speed is higher (right on x), flight length is higher? Wait, no, wait the plot: let's see the trend. Wait, no, maybe I misread. Wait, the options: option d says curved shape and negative? No, wait, let's re - examine. Wait, the scatterplot: as average speed (x) increases, flight length (y) increases? Wait, no, the points: when x (speed) is small, y (flight length) is small; when x is large, y is large? But the options: option d: curved shape and negative? No, wait, maybe the axes are reversed? Wait, no, the problem says "relationship between flight length and average speed". So flight length (y) and average speed (x). Wait, looking at the scatterplot, the points seem to have a curved shape, and as speed (x) increases, flight length (y) increases? No, wait, no—wait, the options: option d: "The scatterplot has a curved shape and shows a negative relationship between flight length and speed." Wait, no, maybe I made a mistake. Wait, let's check the options again. Option d: curved shape, negative relationship. Wait, when speed increases, flight length decreases? No, that doesn't make sense. Wait, maybe the axes are labeled differently. Wait, the x - axis is average speed (mph), y - axis is flight length (miles). Wait, if you have a flight, longer flights might have different speeds. Wait, maybe the scatterplot has a curved shape, and as speed increases, flight length first increases then decreases? No, the options: option d: curved shape and negative relationship. Wait, maybe the correct answer is d? Wait, no, let's re - analyze. Wait, the question is which best describes the relationship. Let's check each option:

a. Linear, positive: The points don't form a straight line, so a is wrong.

b. Curved, positive: The trend isn't positive (if positive, as x increases, y increases; but maybe it's negative).

c. Linear, negative: Not linear, so c is wrong.

d. Curved, negative: Wait, no, if curved and negative, as x (speed) increases, y (flight length) decreases. But that doesn't make sense. Wait, maybe I misread the axes. Wait, maybe the y - axis is flight time? No, the problem says flight length. Wait, maybe the scatterplot has a curved shape, and as speed increases, flight length increases, but in a curved way? No, the options: option d is curved and negative. Wait, maybe the correct answer is d? Wait, no, let's look at the scatterplot again. The points seem to form a curve, and as speed (x) increases, flight length (y) decreases? No, that would be negative. Wait, maybe the longer the flight, the lower the speed? That makes sense: longer flights (more miles) might have lower average speeds (due to takeoff, landing, etc.). So as flight length (y) increases, average speed (x) decreases. So the relationship between flight length (y) and average speed (x) is negative (as y increases, x decreases), and the scatterplot has a curved shape. So the scatterplot (with x = speed, y = flight length) would show that as y (flight length) increases, x (speed) decreases, so the plot (x vs y) would have a curved shape and a negative relationship (since x and y are negatively related). So the correct option is d.

Answer:

d. The scatterplot has a curved shape and shows a negative relationship between flight length and speed.