What is the relationship between the direction of the electric field lines and the change in electric equipotential?

Direction of the electric field lines means direction of lower electric potential.

Explanation:

The direction of the electric field tells us the direction to which the electric potential gets smaller. This is because we use a positive charge as a probe to define everything. If this charge goes against the electric field (lets imagine produced by another positive charge) we realize that work must be done to achieve this, thus we are increasing in electric potential. The other way around: going with the electric field would be what this probe positive charge would do, which is falling in the potential, thus going to lower potential values.