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, we can expand the terms on the right side of the equation:
#y - 10 = color(red)(2)(x - 8)#
#y - 10 = (color(red)(2) xx x) - (color(red)(2) xx 8)#
#y - 10 = 2x - 16#
Next, we can add #color(red)(10)# and subtract #color(blue)(2x)# from each side of the equation:
#-color(blue)(2x) + y - 10 + color(red)(10) = -color(blue)(2x) + 2x - 16 + color(red)(10)#
#-2x + y - 0 = 0 - 6#
#-2x + y = -6#
Now, multiply each side of the equation by #color(orange)(-1)#
#color(orange)(-1)(-2x + y) = color(orange)(-1) xx -6#
#(color(orange)(-1) xx -2x) + (color(orange)(-1) xx y) = 6#
#color(red)(2)x + (-color(blue)(y)) = color(green)(6)#
or
#color(red)(2)x - color(blue)(y) = color(green)(6)#
