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, expand the terms in parenthesis on the right side of the equation by multiplying each term within the parenthesis by a negative #1#:
#y - 4 = color(red)(-1)(x - 1)#
#y - 4 = (color(red)(-1) xx x) + (color(red)(-1) xx -1)#
#y - 4 = -x + 1#
Now, add #color(red)(4)# and #color(blue)(x)# to each side of the equation to ensure both the #x# and #y# variables are on the left side of the equation and the constants are on the right side of the equation:
#color(blue)(x) + y - 4 + color(red)(4) = color(blue)(x) - x + 1 + color(red)(4)#
#x + y - 0 = 0 + 5#
#x + y = 5#
Or
#color(red)(1)x + color(blue)(1)y = color(green)(5)#
