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
To transform this equation to Standard Linear form, first, multiply each side of the equation by #color(red)(5)# to eliminate the fraction. We need all coefficients and the constant to be integers:
#color(red)(5)(y + 1) = color(red)(5) xx 4/5(x + 7)#
#color(red)(5)(y + 1) = cancel(color(red)(5)) xx 4/color(red)(cancel(color(black)(5)))(x + 7)#
#color(red)(5)(y + 1) = color(blue)(4)(x + 7)#
Next, we need to expand the terms in parenthesis on each side of the equation by multiplying the terms within the parenthesis by the term outside the parenthesis:
#(color(red)(5) xx y) + (color(red)(5) xx 1) = (color(blue)(4) xx x) + (color(blue)(4) xx 7)#
#5y + 5 = 4x + 28#
Then, we need to move the #x# term to the left side of the equation and the constants to the right side of the equation. Therefore we need to subtract #color(red)(4x)# and #color(blue)(5)# from each side of the equation to accomplish this while keeping the equation balanced:
#-color(red)(4x) + 5y + 5 - color(blue)(5) = -color(red)(4x) + 4x + 28 - color(blue)(5)#
#-4x + 5y + 0 = 0 + 23#
#-4x + 5y = 23#
To complete the transformation the coefficient of the #x# term must be positive. Therefore, we need to multiply each side of the equation by #color(red)(-1)# to accomplish this while keeping the equation balanced:
#color(red)(-1)(-4x + 5y) = color(red)(-1) xx 23#
#(color(red)(-1) xx -4x) + (color(red)(-1) xx 5y) = -23#
#color(red)(4)x - color(blue)(5)y = color(green)(-23)#
