step 1
Find the slope of the given line
x-3y=9
isolate the variable y
3y=x-9
y=(1/3)x-3
the slope of the given line is m=1/3
Remember that, if two lines are parallel, then their slopes are the same
therefore
the slope of the parallel line is m=1/3
step 2
The equation of the line in slope intercept form is equal to
y=mx+b
we have
m=1/3
point(3,-1)
substitute
-1=(1/3)(3)+b
solve for b
-1=1+b
b=-1-1
b=-2
therefore
the equation of the line is
