Answer
(a) $F=\frac{9}{5}C+32$
(b) $C=\frac{5}{9}(F-32)$
(c) $-40^\circ$
Work Step by Step
(a) Given points $(0,32)$ and $(100,212)$, assume $F=mC+b$, we have $m=\frac{212-32}{100-0}=\frac{9}{5}$ and $b=32$, thus we have $F=\frac{9}{5}C+32$
(b) From the above equation, we have $C=\frac{5}{9}(F-32)$
(c) Let $F=C$, we have $F=\frac{9}{5}F+32$, thus $\frac{4}{5}F=-32$ and $F=C=-40^\circ$
