Wave equation (t-x/c) term for string with density change

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mcheung4
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This is about wave reflection and transmission.

For an infinite string with a density change at x=0, consider an incident wave propagating to the right from x = -∞. The most general form is W = A cos(w(t-x/c)+θ), with amplitude A, angular freuqency w, time t, distance x (from origin), wave speed c and phase θ.

I do not understand the term (t-x/c). Shouldn't it be just t since we're starting from infinity? Thanks!
 

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To me it looks like: t=time at your location, -x/c=time required to get from x to the origin at speed c.