In this world an 'equation' is a statement that says that something is equal to itself, it is a meaningless statement. Algebra' is the 'Science' of tautologies. An equation can only be meaningful if the numbers in the equation are sequential. The position on the number line is an abstraction to test an assumption. Remember that the position on the number line is an abstraction used for a specific purpose.
Numbers are quantitative symbols and are therefore used to signify magnitudes.
The only way we can equate numbers graphically is to use the geometric number line. The number line is simply a straight finite line that represents quantities on a one dimensional scale, graphically. The line is an abstraction and the beginning of the line is also the end of the line. The line represents the whole, and segments of the line represent the parts that make up the whole. Parts of the line can be expressed as ratios of the whole, and we refer to them as rational numbers.