Are electric field lines equipotential or perpendicular?

Electric field lines are not equipotential because the equipotential lines are perpendicular to the electric field lines. The equipotential lines are lines that denote everywhere that has the same electric potential, or is subject to the same electric field.

In a system where the electric field flows directly from one plate to another in a straight line, the electric field points directly between the two plates. Because the equipotential lines are perpendicular to the electric field, they are parallel to the plates. In the case of a point charge, the electric field lines point directly out from the point charge in all directions and the equipotential lines are circular rings around the point.