First, we need to find the slope of the line and isolate the y variable.
#y-1=1/3x+2/3 rarr# Use the distributive property to put the equation in ax+b form
#y=1/3x+1 2/3 rarr# Add 1 to each side to isolate the y
From this equation, we can see that your line's slope is #1/3.# That means all lines that are perpendicular to this particular line must have a slope of #-3,# because perpendicular lines always have slopes that are opposites (positive slope, negative slope) and reciprocals (3 and #1/3#, 4 and #1/4,# for example). The opposite of positive #1/3# would be negative #1/3# and the reciprocal would simply be #1/(1/3),# which would simplify to 3.
Your perpendicular line's y-intercept can be anything.
Some examples could be:
#y=-3x+2#
#y=-3x-6#
