Question

How do I give a "parametrization for the curve": the ray with initial point (2,5) that passes through (-1,0)?

Answer 1

Sorry, I was eating..

To parametrize a curve, you are looking for some functions that relate to y and x.

y = f(t)
x = g(t)

Then you just give bounds on t.

The easiest way to do this is to write your original function y = f(x), then let x = t. So you have x = t, y = f(t) as your parametrization.

Answer 2

So I find the equation of this ray, then substitute x with t?
Btw, does it make a difference whether it is a ray or a line?... A line will be able to extend on both sides, but a ray will only extend on one.

Answer 3

Right, so that means that t is limited. \(2 \le t \lt \infty\)

Answer 4

Wouldn't it be \[-\infty < t \le 2\]
Since the initial point is (2,5)?
Do you mind checking my work? I got
\[y=\left(\begin{matrix}5 \\ 3\end{matrix}\right)t+\left(\begin{matrix}25 \\ 3\end{matrix}\right)\]
x=t
and \[-\infty < t \le 2\]