We can send faxes but we can not receive faxes. The fax machine that sends the fax tell it that our line is busy. Is that a machine problem or a phone line problem?

Problem lies in your Receive Mode setting. If you don't have a dedicated phone line for the fax machine, you need to set it up for either Manual where you answer every call or Fax/Tel whereby the Fax machine determines if the incoming call is a fax or phone call. Instructions per Intellifax 4100 Manual.

Select a Receive Mode
Choose the mode that best suits your needs by pressing the Mode button
repeatedly until the FAX and FAX/TEL lights show the setting you want to use.
Manual
You must answer every call yourself.
The Brother machine must be started manually
to receive faxes.
Fax
For use with a dedicated fax line.
Every call is answered as a fax.
Fax/Tel
For receiving fax and voice calls on one line.
The FAX answers every call and receives a fax or
double rings for you to pick up a voice call.
TAD
For use with an answering device.
The TAD answers every call and stores voice messages.
Fax messages are printed.