This is, by the way, an exercise in "projective coordinates" where we represent the point (x) as the pair (x, 1) with the understanding that the pair (a, b) is equivalent to (a/b, 1).
That allows us to combine both multiplication and addition or subtraction as a single matrix multiplication. For example,
a multiplication by a and an addition of b.
So C= (5/9)(F- 32)= (5/9)F- 160/9, multiplying F by 5/9 and then adding -160/9 can be done by