Remember the Slinky is just a spring that stretches easily.
How stiff a spring is represented by the spring constant, k
k is measured in newtons force over meters (US units pounds/foot)
the slinky's k is very low and its mass is BIG
Most springs can send waves down [along] their length [longitudinal wave,
but the waves are usually too small to see
and too fast to distinguish.
But with Slinky's low k and big mass, the waves down the length slowly
and they easy to see.
Slinky's LOVE to vibrate or swing against their axes and can have large oscillations -
over two feet in amplitude.
These transverse waves [like water waves] shake the Slinky in a direction
perpendicular to its length.