I apologize if the question is elementary, I am having problems understanding if what I am doing is correct.
Write parametric formulas $x(u), y(u) $for the ray cast from the point with coordinates $(1, 2)$ through the point with coordinates $(4, 7)$. Define the domain for the parameter u.
My thought process :
Firstly, I'll use a Parametric Representation of a straight line, $P = P1 +u (P2 − P1)$ to begin.
Next, I'll sub in the values into the formula, giving me the following :
$ - x(u) = 4 +u(1−4) = 4 - 3u$
$ - y(u) = 7 +u(7−2) = 7 + 5u$
and the domain of u will be $[-∞ , ∞ ]$
Forgive me if this question seems elementary, I am not very sure if this is the correct way of answer this question, I am assuming the ray cast would be a straight line, or if I should use slope intercepts instead.
You are incorrect because the ray is cast at $(1,2)$ so at $t=0$, it has to be there.
Find a vector in our direction:
$(4,7)-(1,2)=(3,5)$. Then use our initial point. So
$(1,2) + (3,5)t$ which models our ray.
The domain would start at $t=0$ and go to infinity. Since the ray cannot go backwards.
Note that I assumed that they ray does not stop at $(4,7)$. As the question did not indicate it and only told us that it goes through that point.