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
To transform this equation to standard form, first, multiply each side of the equation by #color(red)(3)# to eliminate the fractions:
#color(red)(3) xx y = color(red)(3)(-1/3x - 9)#
#3y = (color(red)(3) xx -1/3x) - (color(red)(3) xx 9)#
#3y = (cancel(color(red)(3)) xx -1/color(red)(cancel(color(black)(3)))x) - 27#
#3y = -1x - 27#
Next, add #color(red)(1x)# to each side of the equation to place the #x# and #y# variables on the left side of the equation as the standard form requires:
#color(red)(1x) + 3y = color(red)(1x) - 1x - 27#
#1x + 3y = 0 - 27#
#color(red)(1)x + color(blue)(3)y = color(green)(-27)#
