Question

Why do you think we need a horizontal axis and a vertical axis?

Answer 1

A vertical line on a sheet of lined graph paper is a vertical axis (normally called the X axis) that denotes everything to the left of the line is negative and everything to the right is positive. A horizontal line on that graph paper (normally called the Y axis) denotes everything below the line is negative and every thing above is positive. Each axis is graduated in scale. The equation X=Y has no single answer, but we can plot a locus of points on your graph by assigning values to X ( or Y) and create a diagonal line which passes thru the origin (where the lines cross) that denotes all possible answers to the equation that exist within the limits of the graph paper. Every equation will plot a locus of points.