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 the equation in the problem to standard form, first, subtract #color(red)(3x)# from each side of the equation to move the #x# term to the left side of the equation while keeping the equation balanced:
#-color(red)(3x) + y = -color(red)(3x) + 3x + 1#
#-3x + y = 0 + 1#
#-3x + y = 1#
Now, multiply each side of the equation by #color(red)(-1)# to make the coefficient of the #x# term positive:
#color(red)(-1)(-3x + y) = color(red)(-1) xx 1#
#(color(red)(-1) xx -3x) + (color(red)(-1) xx y) = -1#
#color(red)(3)x - color(blue)(1)y = color(green)(-1)#
