The sterplot shows the relationship between two variables, x and y . The sterplot has 10 data points. The data

Question

The sterplot shows the relationship between two variables, $x$ and $y$ .

Which of the following equations is the most appropriate linear model for the data shown?

Accepted Answer

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 + b x , 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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