Question: Approximating a data cloud boundary

Dear colleagues,

I need to determine a linear boundary of a data cloud. More specifically:

I have a set of experimental points y(x). On the plane x-y, the data points form a cloud of a triangular shape, with the legs coinciding with the x and y axes.  I need to best-fit the outer (upper-right), boundary of the data cloud, i.e. the hypotenuse of the "triangle",    with a linear function. It is not necessary for the line to go through the boundary points exactly, I need a best-fitting approximation (actually, the gradient of the line). Could someone give me any idea how to do it? (Or, at least, advice how I can google it, as my searches like "approximate boundary data cloud" return loads of irrelevant stuff.

Thanks in advance!