<PAGE>   1
                                                                    EXHIBIT 10.1



                  FIRST AMENDMENT TO LINE OF CREDIT AGREEMENT

       THIS FIRST AMENDMENT TO LINE OF CREDIT AGREEMENT (this "First Amendment")
is made and entered into as of this 12th day of November, 1997 by and among RARE
HOSPITALITY INTERNATIONAL, INC. (formerly known as LongHorn Steaks, Inc.), a
corporation organized under the laws of Georgia ("RHI" or the "Borrower"), and
FIRST UNION NATIONAL BANK (formerly known as First Union National Bank of
Georgia), as Lender.

                              Statement of Purpose

     The Lender agreed to extend certain Loans to the Borrower pursuant to the
Line of Credit Agreement dated as of December 18, 1996 by and among the
Borrower and the Lender (as amended or supplemented from time to time, the
"Line of Credit Agreement").

       The parties now desire to amend the Line of Credit Agreement in certain
respects on the terms and conditions set forth below.

       NOW THEREFORE, for good and valuable consideration, the receipt and
adequacy of which are hereby acknowledged, the parties hereto agree as follows:

       1.     Effect of Amendment. Except as expressly amended hereby, the Line
of Credit Agreement and Loan Documents shall be and remain in full force and
effect.

       2.     Capitalized Terms. All capitalized undefined terms used in this
First Amendment shall have the meanings assigned thereto in the Line of Credit
Agreement.

       3.     Modification of Line of Credit Agreement. Section 1.1 of the Line
of Credit Agreement is hereby modified by deleting the defined term "Commitment"
and substituting the following in lieu thereof:

              "'Commitment' means the obligations of the Lender to make Loans to
       the Borrower hereunder in an aggregate principal amount at any time
       outstanding not to exceed $5,000,000."

       4.     Conditions. The effectiveness of the amendments set forth herein
shall be conditioned upon delivery to the Lender of the following items:

              (a) Note. The Borrower shall issue and deliver to the Lender, in
       exchange for the Note outstanding, anew Note, payable to the Lender in
       the amount of the Lender's Commitment.

              (b) Officer's Certificate. The Lender shall have received a
       certificate from the chief executive officer or chief financial officer
       of the Borrower to the effect that (after giving effect to this First
       Amendment and the First Amendment to Credit Agreement of even date
       herewith by and among the Borrower and certain of its subsidiaries, the
       Lenders party thereto and First Union National Bank, as Agent) (i) all
       representations and warranties of the Borrower contained in the Line of
       Credit Agreement and the other Loan Documents are true, correct and
       complete in all material respects, except to the extent that such
       representations and warranties expressly relate to an earlier date (in
       which case such representations and warranties shall have been true and
       correct in all material respects on and as of such earlier date); (ii)
       the Borrower is not in violation of any of the covenants contained in the
       Line of Credit


<PAGE>   2



       Agreement and the other Loan Documents; (iii) no Default or Event of
       Default has occurred and is continuing and (iv) the Borrower has
       satisfied each of the closing conditions to be satisfied thereby.

              (c) Certificate of Secretary of the Borrower. The Lender shall
       have received a certificate of the secretary or assistant secretary of
       the Borrower certifying that attached thereto is a true and complete copy
       of the articles of incorporation of the Borrower and all amendments
       thereto, certified as of a recent date by the appropriate Governmental
       Authority in its jurisdiction of incorporation; that attached thereto is
       a true and complete copy of the bylaws of the Borrower as in effect on
       the date of such certification; that attached thereto is a true and
       complete copy of resolutions duly adopted by the Board of Directors of
       the Borrower authorizing the borrowings contemplated under the Line of
       Credit Agreement, as amended hereby, and the execution, delivery and
       performance of the First Amendment and the other Loan Documents to be
       executed in connection herewith; and as to the incumbency and genuineness
       of the signature of each officer of the Borrower executing this First
       Amendment and the other Loan Documents to be executed in connection
       herewith.

              (d) Certificate of Good Standing. The Lender shall have received a
       long-form certificate as of a recent date of the good standing of the
       Borrower under the laws of its jurisdiction of organization.

              (e) Opinion of Counsel. The Lender shall have received a favorable
       opinion of counsel to the Borrower addressed to the Lender with respect
       to the Borrower and the Loan Documents reasonably satisfactory in form
       and substance to the Lender.

       5.     Representations and Warranties/No Default. By its execution
hereof, the Borrower hereby certifies that (after giving effect to this First
Amendment and the First Amendment to Credit Agreement of even date herewith by
and among the Borrower, certain of its Subsidiaries, the Lenders party thereto
and the First Union National Bank, as Agent) each of the representations and
warranties set forth in the Line of Credit Agreement and the other Loan
Documents is true and correct in all material respects as of the date hereof as
if fully set forth herein, except to the extent that such representations and
warranties expressly relate to an earlier date (in which case such
representations and warranties shall have been true and correct in all material
respects on and as of such earlier date), and that as of the date hereof no
Default or Event of Default has occurred and is continuing.

       6.     Expenses. The Borrower shall pay all reasonable out-of-pocket
expenses of the Lender in connection with the preparation, execution and
delivery of this First Amendment, including without limitation, the reasonable
fees and disbursements of counsel for the Lender.

       7.     Governing Law. This First Amendment shall be governed by and
construed in accordance with the laws of the State of North Carolina.

       8.     Counterparts. This First Amendment may be executed in separate
counterparts, each of which when executed and delivered is an original but all
of which taken together constitute one and the same instrument.

       9.     Effective Date. Once executed by each of the parties hereto, this
First Amendment shall become effective as of September 27, 1997.




<PAGE>   3




     IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to
be duly executed as of the date and year first above written.


[CORPORATE SEAL]                           RARE HOSPITALITY INTERNATIONAL,
                                           INC.

                                           By:
                                               ---------------------------
                                           Name:
                                                --------------------------
                                           Title:
                                                  ------------------------


                                           FIRST UNION NATIONAL BANK

                                           By:
                                               ---------------------------
                                           Name:
                                                --------------------------
                                           Title:
                                                  ------------------------