The Connecticut Housing Finance Authority shall develop and administer a program of mortgage assistance to certified teachers (1) employed by priority school districts pursuant to § 10-266p, (2) employed by transitional school districts pursuant to § 10-263c, (3) employed by the Technical Education and Career System at a technical education and career school located in such priority or transitional school districts, (4) who teach in a subject matter shortage area pursuant to § 10-8b, (5) who graduated from a public high school in an educational reform district, as defined in § 10-262u, or (6) who graduated from an historically black college or university or a Hispanic-serving institution, as those terms are defined in the Higher Education Act of 1965, P.L. 89-329, as amended from time to time, and reauthorized by the Higher Education Opportunity Act of 2008, P.L. 110-315, as amended from time to time. Such assistance shall be available to eligible teachers for the purchase of a house as their principal residence, provided, in the case of a teacher employed by a priority or a transitional school district, or by the Technical Education and Career System at a technical education and career school located in a priority or transitional school district, the house is located in such district. In making mortgage assistance available under the program, the authority shall utilize down payment assistance or any other appropriate housing subsidies. The terms of any mortgage assistance shall allow the mortgagee to realize a reasonable portion of the equity gain upon sale of the mortgaged property.