c = (F - 32)5/9 ....(1)
c = k - 273.15 ......(2)
From equation (1);
F = 9c/5 + 32
Substitute equation (2) for C
F = (9(k - 273.15))/5 + 32
F = 9/5k - (9 x 273.15)/5 + 32
F = 9K/5 - 491.67 + 32 = 9K/5 - 459.67
9K/5 = F + 459.67
K = (F + 459.67)5/9
Test: Let T = 32°F
K = (32 + 459.67)5/9 = 273.15