The correct option is A y(x,t)=2 sin(πx4−πt)metres
Let equation of the wave is
y=Asin(ωt−kx+ϕ0)
The particle at origin is moving downwards (from graph) at t=0, so ϕ0=π. Also A = 2 m from graph.
From graph,λ=8m,so k=2πλ=π4
ω=vk=4×π4=π
Putting all the values
y=2 sin[πt−π4x+π]⇒y=2 sin[π4x−πt]