A change of flux in a closed circuit induces an emf and sets up a current. The direction of this current is such that its magnetic field tends to oppose the change of flux. See diagram below.
The direction of the induced emf as given by Lenz's Law may be shown in our equation by introducing a negative sign, but remember that the negative sign is vectorial and not arithmetic.
This formula is not strictly correct. A conductor must cut 108 lines of flux per second in order to induce 1 volt. That is the flux must be changing at a rate of 108 lines per second. The formula should therefore be written as: