The scatterplot shows the relationship between two variables, x and y. y 10+-+--+--+--i------,f-----+---+--+--+--+ 9 ---+--+--i------,f-----+---+--+--+--+ 8 -+---+--+-4~o--+---+---+---+--+--+---+---+- 7 -+---+--+--+--+-----,,-----+---+---+---+----+- 6 +--+--+--+--i------,f-----+---+--+--+--+ 5 +--+--+----t----+if-----+---+--+--+--+ 4 3^-+---+--+--+--+-----,,-----+---+---+---+----+- -+---+--+--+--+-----,re-----+-11-r-t<-.-+---+----+- 2 +--+--+--+--i------,f-----+---+--+--+---.+- -----------------x 1 -+---+--+--+--+-----,,-----+---+---+___,_---+- U 12345678910 Which of the following equations is the most appropriate linear model for the data shown?
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice D is correct. The data points suggest that as the variable x increases, the variable y decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when x is close to 0, y is greater than 9. Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than 9. The graph of an equation of the form = + y a bx, where a and b are constants, has a y-intercept with a y-coordinate of a and has a slope of b. Of the given choices, only choice D represents a graph - that has a negative slope, 0.9, and a y-intercept with a y-coordinate greater than 9, 9.4. Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than 1, not greater than 9. Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than 1, not greater than 9. Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.
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