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 convert to Standard Form for a linear equation, first, subtract #color(red)(1/4x)# from each side of the equation to put the #x# and #y# variables both on the left side of the equation while keeping the equation balanced:
#-color(red)(1/4x) + y = -color(red)(1/4x) + 1/4x + 3#
#-1/4x + y = 0 + 3#
#-1/4x + y = 3#
Now, multiply each side of the equation by #color(red)(-4)# to eliminate the fraction and to ensure the #x# coefficient is positive while keeping the equation balanced:
#color(red)(-4)(-1/4x + y) = color(red)(-4) xx 3#
#(color(red)(-4) xx -1/4x) + (color(red)(-4) xx y) = -12#
#(cancel(color(red)(-4)) xx 1/color(red)(cancel(color(black)(-4)))x) - 4y = -12#
#color(red)(1)x - color(blue)(4)y = color(green)(-12)#
