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
We can transform to this form as follows:
#y + 3 = (3 xx x) - (3 xx 2)#
#y + 3 = 3x - 6#
#y + 3 - color(red)(3) - color(blue)(3x) = 3x - 6 - color(red)(3) - color(blue)(3x)#
# - color(blue)(3x) + y + 3 - color(red)(3) = 3x - color(blue)(3x) - 6 - color(red)(3)#
#-3x + y + 0 = 0 - 9#
#-3x + y = -9#
#color(red)(-1)(-3x + y) = color(red)(-1) xx -9#
#(color(red)(-1) xx -3x) + (color(red)(-1) xx y) = 9#
#color(red)(3)x - color(blue)(1)y = color(green)(9)#
