The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#
Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
First, subtract #color(red)(12x)# from each side of the equation to place both the #x# and #y# term on the left side of the equation as required by the standard form:
#-color(red)(12x) + y = -color(red)(12x) + 12x#
#-12x + y = 0#
Because the #x# coefficient must be positive we will multiply each side of the equation by #color(red)(-1)#:
#color(red)(-1)(-12x + y) = color(red)(-1) xx 0#
#(color(red)(-1) xx -12x) + (color(red)(-1) xx y) = 0#
#color(red)(12)x - color(blue)(1)y = color(green)(0)#
#color(red)(A = 12)#
#color(blue)(B = -1)#
#color(green)(C = 0)#
