What is the slope of any line perpendicular to the line passing through #(4,2)# and #(-1,10)#?

1 Answer
Oct 20, 2017

Answer:

#5/8#

Explanation:

First figure out the slope of the line that passes through those points using the slope formula:

#(y_2-y_1)/(x_2-x_1)# where #y_2=10, y_1=2 and x_2=-1, x_1=4#

So:

#(10-2)/(-1-4)=8/-5=#slope

NOTE: You could also let #y_2=2, y_1-10 and x_2=4, x_1=-1#
Which leads to the same answer (thanks Tony B.!):

#(2-10)/(4-(-1))=(-8)/5=#slope

Perpendicular lines always have different signed slopes (meaning if one line's slope is positive, the perpendicular line's slope is negative and similarly negative #-># positive). Thus our slope is positive.

Also perpendicular lines are reciprocals of each other so our new slope is:

#5/8#