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)(3x)# from each side of the equation to place both the #x# and #y# variables on the left side of the equation while keeping the equation balanced:
#-color(red)(3x) + y = -color(red)(3x) + 3x + 5#
#-3x + y = 0 + 5#
#-3x + y = 5#
Now, multiply each side of the equation by #color(red)(-1)# to make the #x# coefficient a positive integer while keeping the equation balanced:
#color(red)(-1)(-3x + y) = color(red)(-1) xx 5#
#(color(red)(-1) xx -3x) + (color(red)(-1) xx y) = -5#
#3x + (-1y) = -5#
#color(red)(3)x - color(blue)(1)y = color(green)(-5)#
