AP Calculus Question

My wife is prepping her students for the AP Calculus exam. Her students have the fundamentals, so now she is guiding them thru past exams, dissecting questions, analyzing the answers. A pattern emerges on most questions. There are four parts questions after the setup.


The first part is usually a simple definition. The next two question parts seem to be trying to test comprehension of the subject. The last part appears to be unworkable by average students. Sometimes they use concepts or tricks that are not obvious or known to calculus students.

Question:

Find values for m and b in the equation: y=mx+b,
that will satisfy the equation: y' = y + 1


Solution:
Taking the derivative of y = mx +b : y' = mx
substituting into y' = y+ 1
m = mx +b +1

At this point everyone is stuck, because there is one equation with 3 variables.
The not so obvious trick is that we are solving for m and b but x could be anything.
So if the term involving x could be made to disappear, say by setting m = 0 then something might be solvable. So substituting in m= 0:
0 = 0 + b + 1

Thus b = -1.

So it is solvable at the end of the day but for the kids taking this exam what should we tell them? This is just a trick question and it really does not illustrate anything related to calculus.