Displacement of a point on a progressive wave

[jack edison]

Homework Statement

Homework Equations

The Attempt at a Solution

I wrote that Y will have a negative displacement, before returning to equilibrium. Why is Y's displacement positive instead?

 

[theodoros.mihos]

This wave traveling to "+" or right direction so the wave function is: $\Psi(x,k) = A\sin(\omega{t} - kx)$.
Simpler, imagine the wave curve traveling to the right.