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, I would multiply each side of the equation by #color(red)(2)# to eliminate the fraction and to ensure all of the coefficients and constants are integers as require by the Standard Form:
#color(red)(2)(y + 7) = color(red)(2) * 1/2(x + 2)#
#(color(red)(2) * y) + (color(red)(2) * 7) = cancel(color(red)(2)) * 1/color(red)(cancel(color(black)(2)))(x + 2)#
#2y + 14 = x + 2#
Next, subtract #color(red)(14)# and #color(blue)(x)# from each side of the equation to place the variables on the left side of the equation and the constant on the right side of the equation:
#-color(blue)(x) + 2y + 14 - color(red)(14) = -color(blue)(x) + x + 2 - color(red)(14)#
#-x + 2y + 0 = 0 - 12#
#-x + 2y = -12#
Now, multiply each side of the equation by #color(red)(-1)# to ensure the #x# coefficient is a non-negative integer:
#color(red)(-1)(-x + 2y) = color(red)(-1) * -12#
#color(red)(1)x - color(blue)(2)y = color(green)(12)#
