The mean number of students per classroom, y, at Central High School can be estimated using the equation y = 0.8636x + 27.227, where x represents the number of years since 2004 and x 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
A. The estimated mean number of students per classroom in 2004
B. The estimated mean number of students per classroom in 2014
C. The estimated yearly decrease in the mean number of students per classroom
D. The estimated yearly increase in the mean number of students per classroom
Content: Heart of Algebra
Objective: You must interpret the slope of an equation in relation to the real-world situation it models. Also, when the models are created from data, you must recognize that these models only estimate the independent variable, y, for a given value of x.
Explanation: Choice D is correct. When an equation is written in the form y = mx + b, the coefficient of the x-term (in this case 0.8636) is the slope. The slope of this linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).