Social Security Fair Reporting Act of 1979 - Amends title II (Old-Age, Survivors and Disability Insurance) of the Social Security Act to require the Secretary of Health, Education, and Welfare to annually certify in a clear and understandable form to each individual whose income is subject to social security taxes the following: (1) the total wages for which the individual has been credited and the portions of such total paid by the employer; (2) the total social security taxes imposed and collected from such individual; (3) the amounts paid into, the amounts paid out of, and the amount of the surplus or deficit in, the Federal Old-Age and Survivors Insurance Trust Fund, the Federal Disability Insurance Trust Fund, and the Federal Hospital Insurance Trust Fund for the latest fiscal year for which that information is available, and the projected surplus or deficit in such Trust Funds for the next ensuing two fiscal years; (4) the number of quarters of coverage credited to such individual, whether such individual is fully insured, and whether such individual is insured for survivor insurance benefits and for disability insurance benefits; and (5) a telephone number and address to which questions regarding the account of the individual can be directed. Directs the Secretary to report to Congress concerning the implementation of this Act.