Question

a park is studying how its population of deer grows over time. the regression line of their data is y = 15x + 1200, where x represents the number of years since the study began and y represents the number of deer. what does the slope of the regression line represent? a. the deer population will reach 1,200 in 15 years. b. the deer population grows by 1,200 every 15 years. c. there were 15 deer in the park at the beginning of the study. d. for every 1 year, the deer population increased by an average of 15. e. for every 1 year, the deer population increased by an average of 1,200.

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the regression line $y=15x + 1200$, $x$ represents the number of years since the study began and $y$ represents the number of deer.

Step2: Interpret the slope

The slope $m = 15$. In the context of the problem, it means that for every 1 - year increase in $x$ (the number of years since the study began), $y$ (the number of deer) increases by 15.

Answer:

D. For every 1 year, the deer population increased by an average of 15.