This paper discusses the problems of slope-estimation and of linear extrapolation when the precision of theY-measurements changes with different values ofx.Tables are presented which show, for each of these problems, the optimum placement ofx-values and the optimum distribution of theNobservations for selected relationships between σ andx.The optimum placements are seen to be the same for the two problems, but for the latter, the optimum distributions depend on the nearness or remoteness of the extrapolation.