I have an undergrad degree in math, a master's in applied math (focusing on MCMC statistical stuff), and a master's degree in electrical engineering (focusing on computer vision), and I did not know this, and it would have taken me more time than was allotted in the interview to derive it for myself. I feel that when I was asked and I said, "I don't know" it was the unequivocally right thing for me to say to capture the status of my knowledge about it, even if I could have derived it with an extended amount of time.
I think this is still fairly obscure, because my first inclination was to do a simple for-loop over the integers between the two end points along one axis, and then compute the floor of the equation of the line evaluated at that point and just check if it was in fact on the line. The context of the interview did not suggest that non-algorithmic thinking was up for discussion, at least at that moment.
In a short period of time, after doing two other programming questions, the idea that a simple formula existed didn't even cross my mind, and in a regular day-to-day job this is absolutely something I would research rather than just know off the top of my head. I'm not saying that as a system engineer or something, but as someone who has always worked directly in a quantitative modeling, statistics, and math capacity, and is seeking that same kind of work going forward.
I don't really know what this means, other than to say that I did a whole bachelor's degree in math, from real analysis to combinatorial algebra, from boundary value problems to the Sylow theorems, from the formal definition of Turing machines to Jordan Canonical Form, and then did 3 more years of graduate level math, and I feel 100% comfortable with myself when I say I never would have independently thought of this GCD-based solution in a short, timed setting.
The fact that I know how to do it now is also 100% artificial, based only on the happenstance of having been asked it in an interview. If I was asked it again, I feel the right thing to do would be to say: "I know how to solve this because I've seen it before, but my solution is superficial, and if you ask me something else in this area, like say what is the intuition behind Pick's Theorem, I will not have any kind of quick command of that topic and would need to research it." Of course, such honesty just gets you rejected, but still I feel it is the most intellectually honest thing to say.