Thread: line, function, moving tangency

Given the line , where k is the y axis intercept and m is the x axis intercept, and the function , where , find a formula for the scalar such that is always tangent to the line for any positive real k and m.

See the attached graph for an illustration. In plain English the question is: if the line moves, what do you have to do to "a" so that af(x/a) is still tangent to the line.

I will now send my answer to the moderators.

Moderator approved CB