Question

Alan and his classmates performed a linear regression analysis on the data set shown below and found that the line of best fit through the data had the equation y=−54x+18. Which of the following equations represents a line that would intersect their line of best fit at a right angle?

Answer 1

Answer:

C. $y=\frac{4}{5}x+7$

Step-by-step explanation:

Alan and his classmates found that the line of best fit through the data had the equation $y=-\frac{5}{4}x+18$

The slope of this line is $m=-\frac{5}{4}$

If a line would intersect this line of best fit at right angles, then the two lines are perpendicular to each other.

The slopes of perpendicular lines are negative reciprocals of each other,

Hence that line must have slope $\frac{-1}{-\frac{5}{4}} =\frac{4}{5}$

Therefore we look for a line whose slope is $\frac{4}{5}$ from the given options.

That line is the third option $y=\frac{4}{5}x+7$