Clive finds that the line of best fit for the data has the equation y = 0.5x + 1.5. Which statement best explains how removing the point (15, 7) would affect the slope of the line of best fit? A) The slope of the line of best fit would decrease because the point lies below the original line of best fit. B) The slope of the line of best fit would decrease because the point lies above the original line of best fit. C) The slope of the line of best fit would increase because the point lies below the original line of best fit. D) The slope of the line of best fit would increase because the point lies above the original line of best fit.

Answer: C) The slope of the line of best fit would increase because the point lies below the original line of best fit.

The line of best fit is a line that best represents the data in a scatterplot. When you draw a line of best fit, you want it to roughly "balance out" the points above and below it on the scatter plot, making sure the points are distributed evenly.

It's easiest to visualize what a point above or beneath the graph would do. A point underneath that line would be "pulling the line down," so it would be decreasing the slope (making the line more horizontal). A point above the line would be "pulling the line up," so it would be increasing the slope. 

1) Figure out where (15, 7) is in relation to the line of best fit. Plug x=15 into y = 0.5x + 1.5 to find where the line is when x=15:
[tex]y = 0.5x + 1.5\\ y = 0.5(15) + 1.5\\ y = 9[/tex]

That means (15, 7) is under the line, since y=7 at x=15 for the point, but y=9 for the graph.

2) Since (15, 7) is under the line, you can imagine it to be "pulling the line of best fit down" and decreasing the slope. If it's removed then the line would become steeper (aka larger slope), making c the answer.

---

Answer: C) The slope of the line of best fit would increase because the point lies below the original line of best fit.