Question

The organizers of a 5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found a negative linear relationship between f and n that is best modeled by the equation f=−1.2n+38.1 . What statement is true? The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes. The model predicts that the finishing time for a runner in a 5k race is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 38.1 minutes. The model predicts that the finishing time for a runner who has run 1.2 previous 5k races is about 1.2 minutes.

Answer 1

Let's interpret this equation. If we have that a runner has 0 races under his belt, he completes the race in 38.1 min. We have that the slope is -1.2 min/race and the intercept at n=0 is 38.1 min. Hence, for every race, the duration of the run decreases by 1.2 min (or increases by -1.2 min).
Lets derive that. Suppose a runner that has run n races, runs once more.
The difference of times is:
(-1.2(n+1)+38.1)-(-1.2n+38.1)=-1.2(n+1)-(-1.2n)= -1.2n-1.2+1.2n=1.2 minutes.
Hence, the correct answer is the first.

Answer 2

The first thing we must do for this case is to define variables.
n = number of 5k races covered
f = end time.
We have the following equation:
f = -1.2n + 38.1
We note that the slope of the line is:
m = -1.2 minutes per race
Therefore, the time decreases 1.2 minutes when the number of races increases n.
Answer:
The model predicts that for each additional race to runner has run, the finishing time decreases by about 1.2 minutes