Question

1. the equation y = 1494x + 40,860 can be used to predict yearly enrollment at the university of michigan, where y is the number of students enrolled and x is the number of years after 2016.

a. interpret the y -intercept of this line in the context of this problem.
b. interpret the slope of this line in the context of this problem.

Explanation:

a. The y - intercept is the value of y when x = 0. In the context of this problem, when x = 0 (i.e., in the year 2016), the value of y = 40,860. So the y - intercept represents the number of students enrolled at the University of Michigan in 2016.
b. The slope of a linear equation y=mx + b is m. Here, m = 1494. The slope represents the rate of change of y with respect to x. In this context, it means that the number of students enrolled at the University of Michigan increases by 1494 each year after 2016.

Answer:

a. The number of students enrolled at the University of Michigan in 2016 is 40,860.
b. The number of students enrolled at the University of Michigan increases by 1494 each year after 2016.