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M:N:MC:2

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PSAT 10

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Heart of Algebra

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The mean number of students per classroom, y, at Central High School can be estimated using the equation y equals 0.8636 x plus 27.227 comma where x represents the number of years since 2004 and x less or equal than 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

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The estimated mean number of students per classroom in 2004

Correct Answer: 
No

The estimated mean number of students per classroom in 2014

Correct Answer: 
No

The estimated yearly decrease in the mean number of students per classroom

Correct Answer: 
No

The estimated yearly increase in the mean number of students per classroom

Correct Answer: 
Yes

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Choice D is correct. When an equation is written in the form y equals m x plus b comma 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 x less or equal than 10 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.

Question Difficulty: 
easy
Objective: 

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.