Given data:
The given equationn of the line is y=3x-9.
The given point is (6,12).
The standard equation of the line is,
y=mx+c
Comapre the given equation with the above equation.
m=3.
The slope of the line which is parallel to the given line is,
m'=m
m'=3
The equation of the line which is parallel to the given line is,
y-12=3(x-6)
y=3x-6.
The slope of the line which is perpendicular to the given line is,
m(m'')=-1
3m''=-1
m''=-1/3
The equation of the line perpendicular to the given line is,
y-12=(-1/3)(x-6)
3y-36=-x+6
3y=-x+42.
Thus, the equation of parallel line is y=3x-6, and the equation of the perpendicular line is 3y=-x+42.