In which case would the particle move in a straight line along the negative direction of y-axis  (i.e., move along -y^)?

Proton released from rest at origin Due to electric field in negative y direction, proton accelerates and acquire a velocity along negative y directionF→electric=qE→​⇒a→y=−qE0j^m​⇒V→y=−qE0tj^mF→ magnetic =qV→y×B→y V→y is antiparallel to B→y∴F→ magnetic =0Thus, due to of electrostatic force only, the proton moves along negative y-direction.