In the given question, if there is a line passing through the origin at a 45° angle, and it is stated that along this line X=Y, then it is tacitly assumed that both variables are in the same unit. Here`s why:

Option 1: Both variables being pure numbers is incorrect because although a pure number can be equal to another pure number, it is not necessary for this to be the case for the line to represent X=Y.

Option 2: The correct assumption is that both variables are in the same units. This is because for an equation like X=Y to be represented on a graph, the units of measurement of both variables must be the same.

Option 3: If the variables were in different units, one could not accurately represent the equation X=Y on a graph as it would distort the ratio or relationship between X and Y.

Option 4: Having at least one variable as a pure number is not a necessary condition for the line to represent X=Y.

So, in conclusion, for a line in an economic diagram to represent X=Y, both X and Y need to be measured in the same unit.