#3y=x-1/2#

The general linear equation is #y=mx+c#.

#m=slope#

#c#=y-intercept

To find a slope of the line from the liner equation, you have to make sure that all values are in order of the general equation of #y=mx+c#

In #3y=x-1/2#, all values are in the correct position already. However, we have to simplify this linear equation further to ensure that our linear equation is #y=mx+c#

#3y# of #3y=x-1/2# has to become #y# of #y=mx+c#

We can do that by dividing #3y=x-1/2# by #3#.

#(3y)/3=(x-1/2)/3#

#y=1/3x-1/6# as we compare this to the general equation of #y=mx+c#, #m# which is the slope is multiplied together with #x#, hence, the slope for #3y=x-1/2# or #y=1/3x-1/6# is #1/3#