If we set β = f (1), then for any real number x, we have f (x) = β x and the graph of this function is the straight line in the plane passing through the origin with slope β.

John U. Farley, Melvin J. Hinich, A Test for a Shifting Slope Coefficient in a Linear Model, Journal of the American Statistical Association, Vol. 65, No. 331 (Sep., 1970), pp. 1320-1329 ...