electromagnetism - Why is the magnetic flux proportional to the current (Inductance)?

I'm trying to understand the reasoning behing this formula, or how to get there, if possible, using Maxwell's equations:

$$\Phi_i = L_i I_i + M_{ij} I_j$$

From the wikipedia page of inductance I got this formula which is basically faraday's law:

$$v(t) = - \frac{d\Phi(t)}{dt}$$

But then they somehow get to this one which is what I don't understand:

$$v(t) = L \frac{d i(t)}{dt}$$

I've tried doing some things with the Maxwell equations but I couldn't really get to anything interesting.