If our …

farplane = 1000;
nearplane = 250;
point = [2,2,500];

… then we could just take the plane equation 0*x+0*y+1*z=nearplane and calculate the intersection of the plane and the line (from [0,0,0] to [2,2,500]). This gives us [1,1,250].

Great but what is the relationship to the perspective projection matrix?

Please, it’s not helpful to just write down some matrix but explain the relationship and why the perspective projection matrix is the way it is. Note, this is the formular and don't forget about the division for perspective is not an explanation, at least not a good one. In fact I coulnd’t find a good explanation online, which explains the relationship in detail.

Thanks