The given equation is #13x+2y=12#
To get this into the form #y=mx+b#
#m# is the slope and #b# is the #y#-intercept.
Solve the given equation for #y# and we would get what we wanted.
#13x+2y=12#
Subtract #13x# from both the sides. This is done to get #y# term all alone on the left side of the equation.
#13x+2y-13x=12-13x#
#2y=12-13x#
We still have a #2# which is multiplied with #y# and we want #y# isolated. For this, we shall use the opposite operation of multiplication which is division.
The next step is to divide both sides by #2#
#(2y)/2=12/2-(13x)/2#
#y = 6 - 13/2x#
Let us rewrite this in the form #y=mx+b#
#y=-13/2x + 6# This is the slope-intercept form of the line.
