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The mean number of students per classroom, y, at Central High School can be estimated using the equation 
where x represents the number of years since 2004 and 
Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
Select an Answer
The estimated mean number of students per classroom in 2004
The estimated mean number of students per classroom in 2014
The estimated yearly decrease in the mean number of students per classroom
The estimated yearly increase in the mean number of students per classroom
View Correct Answer
Choice D is correct. When an equation is written in the form 
the coefficient of the x-term (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).
Choice A is not the correct answer. This answer may result from a misunderstanding of slope and y-intercept. The y-intercept of the equation represents the estimated mean number of students per classroom in 2004.
Choice B is not the correct answer. This answer may result from a misunderstanding of the limitations of the model. Students may see that 
and erroneously use this statement to determine that the model finds the mean number of students in 2014.
Choice C is not the correct answer. This answer may result from a misunderstanding of slope. The student recognizes that slope models the rate of change, but may think that a slope of less than 1 represents a decreasing function.
Students must interpret the slope of an equation in relation to the real-world situation it models. Furthermore, when the models are created from data, students must recognize that these models only estimate the independent variable, y, for a given value of x.