What is the slope of any line perpendicular to the line passing through #(-3,1)# and #(-6,12)#?

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Answer 1 · 2018-04-27T23:49:21

#3/11#

First, let's find the slope through the given two points: #(y_2-y_1)/(x_2-x_1)#, where there are two points #(x_1, y_1)# and #(x_2, y_2)#:

#(12-1)/(-6-(-3))#

#11/(-3)#

#-11/3#

Perpendicular slopes are opposite reciprocals of one another:

Opposites: put a negative sign in front of a positive number or take away a negative sign from a negative number (ex. #-3, 3#, #7/11, -7/11#

Reciprocals: flip the numerator and denominator (ex. #12/5, 5/12#, #4, 1/4#)

The opposite of #-11/3# is #11/3#

The reciprocal of #11/3# is #3/11#