I thought he said the question specifically asks "for the equation as a function of y in terms of x"? However, his final answer was in terms of y (the last line) the teacher might deduct mark, don't you think?
In the HSC, the marking is always done with the benefit of the doubt given to the student. It is also done with the mindset of awarding marks, not deducting marks.
For example, if the student does the working leading up to the correct answer say:
<working>
y = x + 1
x = y - 1
then as far as the marker is concerned, the student has demonstrated the required knowledge to get to the correct answer y = x + 1.
The line x = y - 1 is seen as an unnecessary line that adds no value to
gaining marks. It is not seen as “another answer”. Therefore, the student is awarded full marks.
The only time a “deduction” may occur is when there is a logical contradiction. For example, if the student gets y = x + 1 but also says y = x - 1 through an alternative method, but does not demonstrate which one is correct. This scenario is what I think the OP was more likely referring to.
Keep in mind, this is for HSC marking of the external exams. For internal assessments, teachers can enforce whatever marking criteria they want.