Question

parametric equation of the line passes through (2,1) and (3,0) is x = 2+t and y = 1-t.
My question is how to consider the condition of t?
Please , help

Answer 1

actually, it's just a part of the whole question, i don't understand just this part, so i pick it out to ask, if you want to know the whole thing, I will edit the question

Answer 2

what do you mean "condition for t"?

Answer 3

in class, my prof give out the parametric equation like that and 0<=t<=1 , i don't know why

Answer 4

because I have to use that limit to construct an integral.

Answer 5

ok, let me post the original problem.

Answer 6

that's what I study in class, now apply to homework, I don't know how my prof get that limits of t to construct the int

Answer 7

So our x ranges from \(\large 2\) to \(\large 3\).
And our y ranges from \(\large 1\) to \(\large 0\).

Let's plug these into our parametric equations, to find the interval for \(\large t\).
We really only need to check one of them. Either checking x or y will give us the same t values.

\[\large x=2+t\]So x starts at 2,\[\large 2=2+t\]Solving for \(\large t\) shows us that \(\large t\) starts at \(\large 0\).

the end of the interval is x=3,
\(\large 3=2+t\)

So we can determine that the interval of \(\large t\) is,
\(\large 0\le t\le 1\)
right?

Answer 8

Is that the part you were confused on?

Answer 9

oh good c:

Answer 10

thank you very much, zepdrix