Well!!!
Let us assume A F + B = C ---- {1}
59F equals 15C ==> 59 A + B = 15 ......{2}
68F equals 20C ==> 68 A + B = 20.... {3}
Solving {2} and {3},
{3} - {2} ==> 9 A = 5 ==> A = 5/9
{2} ==> B = 15 - 59 A = 15 - 59 (5/9) = -160/9
Thus, the Equation for conversion: C = 5/9 F - 160/9 = 5 (F - 32) / 9
Now, at 77 F , C = 5(77-32)/9 = 25 deg C