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The average number of students per classroom, \( y \), at Central High School can be estimated using the equation \( y=0.8636 x+27.227 \), where \( x \) represents the number of years since 2004 and \( x \leq 10 \). Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
A) The estimated average number of students per classroom in 2004
B) The estimated average number of students per classroom in 2014
C) The estimated yearly decrease in the average number of students per classroom
D) The estimated yearly increase in the average number of students per classroom
in Mathematics by Platinum (108k points) | 17 views

1 Answer

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Choice D is correct. When an equation is written in the form \( y=m x+b \), the coefficient of the \( x \)-term (in this case 0.8636 ) is the slope of the graph of this equation in the \( x y \)-plane. The slope of the graph of this linear equation gives the amount that the average number of students per classroom (represented by \( y \) ) changes per year (represented by \( x \) ). The slope is positive, indicating an increase in the average number of students per classroom each year.

Choice A is incorrect and may result from a misunderstanding of slope and \( y \)-intercept. The \( y \)-intercept of the graph of the equation represents the estimated average number of students per classroom in 2004.

Choice B is incorrect and may result from a misunderstanding of the limitations of the model. You may have seen that \( x \leq 10 \) and erroneously used this statement to determine that the model finds the average number of students in 2014.

Choice \( \mathrm{C} \) is incorrect and may result from a misunderstanding of slope. You may have recognized that slope models the rate of change but thought that a slope of less than 1 indicates a decreasing function.
by Platinum (108k points)

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