A line parallel to another line #ax+by+c=0# is #ax+by=k_1#, where #k_1!=-c#. Further a line perpendicular to #ax+by+c=0# is #bx-ay=k_2#, where #k_2# is another constant.
Note that for parallel line coefficients of #x# and #y# remain same but constant term changes. However, for a perpendicular line, coeffcients are interchanged and sign of one changes. Observe that this leads to slopes of parallel lines as equal and product of slopes of two perpendicular lines being #-1#.
Using this
(a) A line parallel to #y=2x-4# is #y=2x+3#, say and a line perpendicular to it is #2y=-x-5# or #y=-1/2x-5/2#
(b) A line parallel to #y=-x+5# is #y=-x+1#, say and a line perpendicular to it is #y=x-5#
(a) A line parallel to #y=1/3x-2# is #y=1/3x+3#, say and a line perpendicular to it is #1/3y=-x+2# or #y=-3x+6#
