Recently, there is this question on our exam paper (Secondary level):
Find the real number $r$ such that the equation: $$y=\frac{r}{r+3}x+\frac{4}{r+3}$$ is parallel with the y-axis.
The answer key for this question give $r=-3$, and the explanation says that for a line to be parallel with the y-axis, its gradient must be undefined.
I want to ask whether it is true (my answer for this question is that there is no real number $r$ satisfy the requirement) and the same concept holds at higher level (in college and university). Thank you!
If the equation had been written $$(r+3)y=rx+4$$ then a solution for the problem would be $r=-3$. As it is the equation does not define anything for $r=-3$.
At tertiary level you would expect the question to be more carefully defined, and if given as stated you might expect a trick question. At secondary level you need to make allowances for some imprecision, in both textbooks and teaching. Remember that the purpose of an exam is to assess your knowledge, so an answer showing that you understand both the gradient issue and the division by zero issue would be best.