Let #r# and #s# be to lines, and #m_r# and #m_s# their slopes. The two lines are perpendicular if the following relation holds:

#m_s = -1/m_r#

So, we must find the slope of the line #x-3y=9#, and using the relation wrote above we'll find the perpendicular slope.

To find the slope of a line, we must manipulate its equation in order to bring it into the form

#y=mx+q#

and once in that form, #m# will be the slope. Starting from #x-3y=9#, we can add #3y# to both sides, obtaining #x=3y+9#. Subtracting #9# from both sides, we get #x-9=3y#. Finally, dividing by #3# both sides, we have #y=1/3 x - 3#.

Since our slope is #1/3#, its perpendicular slope will be #-3#