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)(4x)# from each side of the equation to place both the #x# and #y# variables on the left side of the equation as required by the formula:
#-color(red)(4x) + y = -color(red)(4x) + 4x - 7#
#-4x + y = 0 - 7#
#-4x + y = -7#
Now, multiply each side of the equation by #color(red)(-1)# to ensure the #x# coefficient is non-negative while keeping the equation balanced:
#color(red)(-1)(-4x + y) = color(red)(-1) xx -7#
#(color(red)(-1) xx -4x) + (color(red)(-1) xx y) = 7#
#color(red)(4)x + color(blue)(-1)y = color(green)(7)#
Or
#color(red)(4)x - color(blue)(1)y = color(green)(7)#
Or
#color(red)(4)x - y = color(green)(7)#
