A PA28 INSTRUCTOR AND STUDENT PRACTICING SLOW FLT MANEUVERS HAD AN ENG FAILURE. THEY MADE A SAFE OFF AIRPORT LNDG WITH NO DAMAGE OR INJURIES.

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AFTER CHKING THE WX ON AN AVIATION WEBSITE; I TOOK OFF WITH A CFI STUDENT A LITTLE AFTER XA00. WE WERE IN A PA28-151. OUR RUN-UP AND TKOF WERE NORMAL AND WE HEADED OUT TO THE PRACTICE AREA SE OF THE ARPT. WHEN WE GOT THERE WE LEVELED OFF AT 4000 FT MSL AND I TOLD HIM TO TEACH ME SLOW FLT. SO HE STARTED TO SLOW DOWN AND HE DID SOME CLRING TURNS. HE TURNED THE FUEL PUMP ON FOR THE MANEUVER; PULLED THE PWR BACK AND ADDED FLAPS. WHEN THE AIRSPD GOT DOWN AROUND 60 KTS HE WENT TO ADVANCE THE THROTTLE BUT NOTHING HAPPENED. THERE WAS NO INCREASE IN THE RPM. THEN I TRIED TO ADVANCE THE THROTTLE AS WELL; AND THERE WAS STILL NO RESPONSE. I TOOK CTL OF THE ACFT; PUT THE FLAPS UP AND PITCHED FOR BEST GLIDE OF 73 KTS. I LEFT THE THROTTLE OPEN AN INCH AND CALLED FOR THE RESTART CHKLIST. HE DID THE CHKLIST AND READ EACH ITEM OUT LOUD AND WE VERIFIED AND DID. WHILE HE WAS READING THE CHKLIST I SET UP ON A HIGH BASE TO FINAL FOR A DIRT ROAD W OF THE TOWN. WHEN WE DIDN'T GET A RESTART I HAD HIM SQUAWK 7700 AND PUT IN THE EMER FREQ 121.5. I MADE A CALL DECLARING AN EMER GIVING OUR CALL SIGN; ACFT TYPE; COLOR; MY BEST POS ESTIMATE; AND THAT THERE WERE 2 PEOPLE ON BOARD. SOMEONE ANSWERED BACK AND ASKED WHAT OUR TYPE WAS AND POS. I ANSWERED BACK AND TURNED ON A HIGH FINAL WHERE I STARTED TO ADD IN FLAPS. THEN I HAD HIM DO THE PWR OFF LNDG EMER CHKLIST. WE PULLED THE MIXTURE LAST AND WE WAITED TO DO THAT UNTIL WE WERE 300 FT AGL IN CASE THE ENG CAME BACK ON. WE WERE SET UP PERFECTLY ON FINAL. I MADE A SOFT FIELD LNDG AND THE ACFT TOUCHED DOWN HALFWAY DOWN THE DIRT ROAD WHERE IT EVENTUALLY ROLLED TO A STOP. I PULLED THE KEYS OUT OF THE IGNITION AND WE DIDN'T TOUCH THE CTLS AGAIN. WE WERE ABLE TO CONTACT OUR DISPATCH AND ZZZ TWR AND THEY HELPED US FIGURE OUT WHERE WE WERE. THERE WAS NO DAMAGE TO THE ACFT OR ANY PROPERTY AND MY STUDENT AND I WERE UNHURT.