What is the equation of the line perpendicular to # y=-3/7x+12 # at #x=-1 #?

1 Answer
Apr 2, 2017

Answer:

#y = (7/3)x + (310/21)#

Explanation:

Perpendicular means that the slopes will be opposite, so the slope is (7/3). At x = -1 the original line y value is #12+3/7# or #(87/7)#.
To find the new constant at that point we put it into the new equation.
#y = (7/3)x + b# ; #(87/7) = (7/3)(-1) + b# ; #(87/7) + (7/3) = b# ; #(261/21) + (49/21) = b#

#(310/21) = b#
So the new line equation is #y = (7/3)x + (310/21)#

CHECK: At (-1, (87/7)) #(87/7) = (7/3)(-1) + (310/21)#

#(87/7) = -(49/21) + (310/21)# ; #(87/7) = (261/21)#
#(87/7) = (87/7)# Correct!