This is a point of confusion for me...

When r = 1 or -1 for a set of bivariate data, does that mean that all the points must fall on the standard deviation line (which has a slope of + or -SDy/SDx and passes through the point of averages)? And conversely, when all points fall on the SD line does that mean that r is 1 or -1?

I'm just a little confused on how the SD line relates to correlation. Thanks!