In what ratio is the line joining $(4,5)$ and $(1,2)$ is divided by the y-axis?
The solution given in my module assumed the ratio to be $K:1$,this might be very trivial but I can't convinced myself why the consequent is assumed to be $1$?
It would help to could clarify your question. Lines are normally assumed to be infinite in length (unless otherwise qualified). The line segment from (4,5) to (1,2) is not intersected by the y-axis. Is it possible that one of the x-values should be negative?
As Fabian notes, any ratio can be expressed as K:1. If K happens to be an integer, say, 7, you want to leave in the ":1", expressing it as 7:1 to make clear that it involves a comparison, that is a statement of the relative magnitudes of two quantities. ("7" by itself is not clearly identified as a ratio).