what is the rate of change of the function y=3

Answer 1

That is a horizontal line, changeless forever and ever, no slope at all :)

Answer 2

in y = mx + b, the rate of change or slope is m

consider y = 3 as
y = 0x + 3

so the rate of change is zero, or "y does not change", it is always 3

Answer 3

I think Damon went a bit overboard. The line has a slope, and it is zero.

Not at all the same as having no slope at all. A vertical line's slope is undefined. Hmmm. Is that the same as not having a slope? Not sure...