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

Question

Accepted Answer

Choice B is correct. The equation representing a linear model can be written in the form y = a + bx, or y = bx + a, where b is the slope of the graph of the model and (0, a) is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, b 0. Of the given choices, only choice B, y = −1.9x + 10.1, has a negative value for b, the slope, and a positive value for a, the y-coordinate of the y-intercept. Choice A is incorrect. The graph of this model has a y-intercept with a negative y-coordinate, not a positive y-coordinate. Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y-intercept with a negative y-coordinate, not a positive y-coordinate. Choice D is incorrect. The graph of this model has a positive slope, not a negative slope.

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