Question 976455
slope of this line is chg y/chg x =(3/4)
perpendicular is negative reciprocal or -4/3  That is your answer.

To prove it:
use point slope formula with that

y-y1=(-4/3) (x-x1)
y-6=(-4/3)(x-6)= -(4x/3)+8.  Note, you may use either point.

y=(-4/3)x +14

equation of original line is y=(3/4)x-3/2+3=y=(3/4)x+(3/2)

{{{graph(300,300,-10,10,-10,10,(3x/4)+(3/2),(-4x/3)+14)}}}