we have that
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3
we know that
if two lines are perpendicular
then
m1*m2=-1
m1=3
so
m2=-1/3
with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3
the equation of the line is
y=(-1/3)x+3
the answer is
y=(-1/3)x+3
see the attached figure
