I think SSA is related to CPS, but I'm not sure of the correspondence with Linearity. I think the key difference (but I'm not sure), is that SSA only asserts that a variable is assigned once, but might be consumed multiple times. Linearity says that things must be consumed exactly once. For instance, I think:

y <- x + 1

z <- x + 2

is a legal SSA expression, but it is not a legal linear expression because x appears twice.

(Corrections welcome)

FWIW:

https://www.cs.princeton.edu/~appel/papers/ssafun.ps