Question 48

y = 50x + 100 best represents the line of best fit.

The equation y = 50x + 100 accurately describes the trend in the number of geese at the zoo from 2005 to 2012, as it aligns with the observed data points and shows a consistent increase over the years.

A) y = 20x + 250

This equation suggests a much slower increase in the number of geese, which does not match the trend shown in the scatterplot. The slope of 20 implies fewer geese added per year than what is actually observed.

B) y = 50x + 100

This equation correctly captures the rapid increase in the number of geese at the zoo, with a slope of 50 indicating a significant rise in the population each year, consistent with the data shown in the scatterplot.

C) y = 30x + 150

While this equation represents a positive trend, the slope of 30 is not steep enough to reflect the actual increase in the number of geese as indicated by the scatterplot. The intercept also does not align well with the data points.

D) y = 40x + 200

This equation suggests a reasonable increase but still falls short of accurately representing the data. The slope of 40 does not sufficiently account for the higher growth rate observed between 2005 and 2012.

Conclusion

The equation y = 50x + 100 is the most accurate representation of the line of best fit for the given data, as it reflects the steep increase in the number of geese over the specified years. Other options either understate the growth rate or misplace the intercept, failing to align with the observed trend in the scatterplot.