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, eliminate the fractions by multiplying each side of the equation by #color(red)(2)# while keeping the equation balanced:
#color(red)(2)(y + 2) = color(red)(2) xx 1/2(x - 4)#
#(color(red)(2) xx y) + (color(red)(2) xx 2) = cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))(x - 4)#
#2y + 4 = x - 4#
Next subtract #color(red)(4)# and #color(blue)(x)# to put the #x# and #y# variables on the left side of the equation, the constant on the right side of the equation while keeping the equation balanced:
#-color(blue)(x) + 2y + 4 - color(red)(4) = -color(blue)(x) + x - 4 - color(red)(4)#
#-x + 2y + 0 = 0 - 8#
#-x + 2y = -8#
Now, multiply both sides of the equation by #color(red)(-1)# to ensure the #x# coefficient is non-negative while keeping the equation balanced:
#color(red)(-1)(-x + 2y) = color(red)(-1) xx -8#
#(color(red)(-1) xx -x) + (color(red)(-1) xx 2y) = 8#
#color(red)(1)x - color(blue)(2)y = color(green)(8)#
