What is the slope of the line perpendicular to # y=16/7x-11#?

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Answer 1 · 2016-07-18T10:34:32

#-7/16#

Recall that the slope #m# of a straight line is related to the angle #theta# that it makes with the #X# axis by

#m = tan theta#

Two mutually perpendicular lines obey #theta_2 = theta_1 + pi/2# so that

#m_1 m_2 = tan theta_1 tan theta_2 = tan theta_1 tan (theta_1 + pi/2) = tan theta_1 (- cot theta_1) = -1#

Answer 2 · 2016-07-18T11:02:52

#-7/16#

Consider the standard equation form #y=mx+c# where #m# is the gradient.

Any line perpendicular to this has the gradient of #-1/m#

So for #y=16/7x-11# the gradient of a line perpendicular to this is

#-7/16#