For a particular section of the wave which is moving in any direction, the phase must be constant. So, if the equation says y(x,t)=Acos(ωt+βx+Ï•)y(x,t)=Acos⁡(ωt+βx+Ï•), the term inside the cosine must be constant. Hence, if time increases, xx must decrease to make that happen. That makes the location of the section of wave in consideration and the wave move in negative direction.