Question - Finding the Best-Fitting Equation for Scatterplot Data
Solution:
To find the equation that best fits the data on a scatterplot, we look for the line that closely follows the trend of the data points.From what I can see in the image:1. The slope of the line should be positive, as the points seem to increase as we move from left to right.2. The y-intercept is the point where the line crosses the y-axis. At x = 0, the line should cross the y-axis around the value of 9.This information helps us eliminate some of the options:- Option A ($$y = \frac{1}{2}x + 9$$) has a positive slope and the correct y-intercept.- Option B ($$y = 2x + 9$$) also has a positive slope and the correct y-intercept.- Option C ($$y = \frac{1}{2}x - 9$$) has the correct slope direction but the incorrect y-intercept.- Option D ($$y = 2x + 9$$) is the same as option B, which appears to be an error in the image as it's duplicated and does not provide another distinct option.Now, to distinguish between the remaining options A and B (or D, since it's the same), we need to consider the steepness of the line in the scatterplot. Option A has a gentler slope ($$\frac{1}{2}$$) than Option B (2). By inspecting the graph, it looks like the data points rise slower than a slope of 2 for every increase in x (since a line with slope 2 would rise too steeply for these data points), which suggests that Option A with a slope of $$\frac{1}{2}$$ and a y-intercept at 9 would be the best fit for the data.Thus, Option A, $$y = \frac{1}{2}x + 9$$, is most likely the equation that best fits the data on the scatterplot.
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