Question

which pair of points should be used to find the line of best - fit for the scatterplot?
j and l
j and m
k and l
k and m

Explanation:

Step1: Understand the concept of line of best - fit

The line of best - fit should pass through or be close to the majority of the data points. We need to check the position of each pair of points.

Step2: Analyze pair \(J\) and \(L\)

Point \(J=(1,10)\) is an out - lier (lower than most of the other points). A line through \(J\) and \(L=(11,45)\) will be pulled down by \(J\) and may not represent the trend of the majority of the data points well.

Step3: Analyze pair \(J\) and \(M\)

Since \(J\) is an out - lier, a line through \(J=(1,10)\) and \(M=(12,42)\) will also be affected by the low - value of \(J\) and not be a good representation of the central trend of the data.

Step4: Analyze pair \(K\) and \(L\)

Point \(K=(2,19)\) is relatively low. A line through \(K=(2,19)\) and \(L=(11,45)\) may not be the best as \(K\) is not in the central cluster of most of the data points (which are more in the range \(x = 4\) to \(x=12\) and \(y = 25\) to \(y = 45\)).

Step5: Analyze pair \(K\) and \(M\)

Point \(K=(2,19)\) and \(M=(12,42)\). The line through these two points will pass through or be close to the central part of the data set. The data points are more densely distributed around the line that would be formed by connecting \(K\) and \(M\) compared to the other pairs (because \(J\) is a clear out - lier and using \(J\) will deviate the line from the central trend of the data)

Answer:

\(K\) and \(M\)