add or subracting equation

Imagine a grid ... there is an origin and the two grid lines it is on are labelled X and Y. The X axis is labelled +1,+2,+3,+4,+5 ... going one way and -1,-2,-3,-4,-5 ... going the other way. Label the Y axis in the same way. Let these two axes be defined as the principal axes. Let the X and Y Values of any intersection be be the values on the principal axes that the grid lines connect a given point to the principal axes pass through. For those points where X and Y are posative label the intersection with the product of X and Y. You now have a pattern. Extend the patern to the principal eaxes and beyond and in the two newly populated quadrents you find all the numbers are -ve. By a simelar extensio to the 4th quadrent you find you have +ve numbers here. The rule of signs in multipication is simply a reflection of this pattern.