OG详解-OG6 数学2 Q26

Choice A is correct. An equation of a line of best fit for data set F can be written in the form y = a+bx, where a is the y-coordinate of the y-intercept of the line of best fit and b is the slope. The line of best fit shown for data set E has a y-intercept at approximately (0, 12). It’s given that data set F is created by multiplying the y-coordinate of each data point from data set E by 3.9. It follows that a line of best fit for data set F has a y-intercept at approximately (0, 12(3.9)), or (0, 46.8). Therefore, the value of a is approximately 46.8. The slope of a line that passes through points (x₁, y₁) and (x₂, y₂) can be calculated as y2−y1x2−x1​​ . Since the line of best fit shown for data set E passes approximately through the point (12, 30), it follows that a line of best fit for data set F passes approximately through the point (12, 30(3.9)), or (12, 117). Substituting (0, 46.8) and (12, 117) for (x₁, y₁) and (x₂, y₂), respectively, in y2−y1x2−x1yields 117−46.812−0​​, which is equivalent to 70.212​​, or 5.85. Therefore, the value of b is approximately 5.85, or approximately 5.9. Thus, y = 46.8+5.9x could be an equation of a line of best fit for data set F.
Choice B is incorrect and may result from conceptual or calculation errors.Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This could be an equation of a line of best fit for data set E, not data set F.