Technically you should use "substitution" in place of "transitive property of equality", though they are very closely related ideas. If I were your teacher, then I would accept that answer as valid nonetheless.
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Substitution says that if a = b and c = b, then a = c. We replace the 'b' in a = b with 'c'. Think of your substitute teacher who replaces your current teacher for a temporary basis. This is how to remember the term "substitution.
On the other hand, the transitive property of equality says that if a = b and b = c, then a = c. The equations chain together and can simplify into one single equation.
