OG详解-OG8 数学1 Q11

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. The scatterplot also shows that the data points are close to the y-axis at a positive value of y. Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means a > 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.