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, multiply each side of the equation by #color(red)(6)# to eliminate the fractions while keeping the equation balanced:
#color(red)(6)(y - 1) = color(red)(6) xx 5/6(x - 4)#
#color(red)(6)(y - 1) = cancel(color(red)(6)) xx 5/color(red)(cancel(color(black)(6)))(x - 4)#
#(color(red)(6) xx y) - (color(red)(6) xx 1) = 5(x - 4)#
#6y - 6 = (5 xx x) - (5 xx 4)#
#6y - 6 = 5x - 20#
Next, add #color(red)(6)# and subtract #color(blue)(5x)# from each side of the equation to isolate the constant on the right side of the equation while keeping the equation balanced:
#-color(blue)(5x) + 6y - 6 + color(red)(6) = -color(blue)(5x) + 5x - 20 + color(red)(6)#
#-5x + 6y - 0 = 0 - 14#
#-5x + 6y = -14#
Now multiply each side of the equation by #color(red)(-1)# to make the #x# coefficient positive while keeping the equation balanced:
#color(red)(-1)(-5x + 6y) = color(red)(-1) xx -14#
#(color(red)(-1) xx -5x) + (color(red)(-1) xx 6y) = 14#
#5x + (-6y) = 14#
#color(red)(5)x - color(blue)(6)y = color(green)(14)#
