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, subtract color(red)(12x) from each side of the equation to place both the x and y term on the left side of the equation as required by the standard form:
-color(red)(12x) + y = -color(red)(12x) + 12x
-12x + y = 0
Because the x coefficient must be positive we will multiply each side of the equation by color(red)(-1):
color(red)(-1)(-12x + y) = color(red)(-1) xx 0
(color(red)(-1) xx -12x) + (color(red)(-1) xx y) = 0
color(red)(12)x - color(blue)(1)y = color(green)(0)
color(red)(A = 12)
color(blue)(B = -1)
color(green)(C = 0)
