Explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another. it is constant anywhere on a line.
the easiest example is therefore to go from point (x, y) to the point of x+1. we see here that the point at x+1 gives us also y+1.
so, the change of x and y coordinates is equal.
therefore, the slope is 1.