The equation of the line of best fit shown on the scatter plot is f(x)=10.2217−0.0098x

Question

, where 𝑓 is the finishing time of the Olympic gold medalist in the men’s 100 m dash, and 𝑥 is the number of years since 1960.(1 point)
Part A: Interpret the 𝑦-intercept of the linear equation modeling the data.

The model suggests that the finishing time of the Olympic gold medalist in the men’s 100 m dash in 1960 was
seconds

Part B: Interpret the slope of the linear equation that models the data.

The finishing time since 1960 has decreased each year by
seconds

Part C: The Summer Olympic Games, where the 100 m dash is run, occur every 4 years. By how many seconds does the model predict the first-place-finishing time will decrease every 4 years?

seconds.

Answer 1

To interpret the given linear equation \( f(x) = 10.2217 - 0.0098x \):

Part A: Interpret the \( y \)-intercept

The \( y \)-intercept occurs when \( x = 0 \). In this case, \( f(0) = 10.2217 - 0.0098(0) = 10.2217 \). This means that the model suggests that the finishing time of the Olympic gold medalist in the men’s 100 m dash in 1960 was 10.2217 seconds.

Part B: Interpret the slope

The slope of the line is \(-0.0098\). This indicates that for every year after 1960, the finishing time of the Olympic gold medalist in the men’s 100 m dash is predicted to decrease by 0.0098 seconds.

Part C: Time prediction over 4 years

Since the Olympic Games occur every 4 years, we multiply the slope by 4 to find the predicted decrease over that period:

\[ \text{Decrease in time over 4 years} = 4 \times (-0.0098) = -0.0392 \text{ seconds} \]

Thus, the model predicts the first-place-finishing time will decrease by 0.0392 seconds every 4 years.