The line of best fit for the data presented in the scatterplot is y = 0.5x. (Option B)
A line of best fit represents a straight line that is the best approximation of the given set of data used to examine the nature of the relation between two variables. It is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot. The slope-intercept form of a linear equation is given by y = mx + b where m is the slope of the line and b is the y intercept of the graph. For any two points (x1, y1) and (x2, y2), the slope is given by:
m = (y2-y1)/(x2-x1)
Choosing two points from the line say (180, 90) and (220,110),
m = (110 – 90)/(220 – 180) = 20/40 = 0.5
Hence, y = 0.5x + b
Substituting a point from the graph into the equation say (240, 120)
120 = 0.5(240) + b
120 = 120 + b
b = 0
Hence, the equation is y = 0.5x
Note: The question is missing the scatterplot (which is attached) and options which are A. y = -0.5x, B. y = 0.5x, C. y = -2x, D. y = 2x.
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