and it is reflected across the line y=x, the
slope of the resulting line is 1/m. The reason for this is that if the
points (a,b) and (c,d) are on the original line then the points (b,a) and
(d,c) are on the reflected line. It is easy to see that the original slope
is (d-b)/(c-a) while the slope of the new line is the reciprocal:
(c-a)/(d-b). Since a line should be tangent to a curve regardless of the
coordinate system, and the graph of an inverse function is found by reflecting
the graph of the original function over y = x, the tangent line should come
along for the ride. Here are some examples to make this concrete.