how do you solve for a parametric equation using 2 points?

Question

i asked this question before, and people gave me the right answer, i just dont know how to get the answer.
for example, you have two points, (0,0) and (5, -2).
HOW do you figure out the equation?
I KNOW what the answer is, i need an explanation.
THANKS!!!!!

thanks! but what is A1?

The question asks to find the parametric equation that runs through those 2 points. It is a line.

Answer 1

Parametric equations are as follow:

x = X1 + A1t
y = Y1 + A2t
z = Z1 + A3t

Answer 2

If there is a parametric equation, it would help to know what that is. If it is a straight line through these two points the answer is trivial, and here it is:
y(x)=ax+b
y(0)=a(0)+b=0, so b=0
y(5)=5a+0=-2
a=-2/5
If I have trivialized this too much I am sorry.

Answer 3

a million) r(t) = (3t-2)i + (4t+3)j r'(t) = 3i + 4j arc length = ??(3^2+4^2)dt = 5t 2) r(t) = (tcost)i + (tsint)j + (2/3)(sqrt(2))(t^(3/2))ok ; t>=0 r'(t) = (value - tsint)i + (sint + tcost)j + (sqrt(2))(t^(a million/2))ok (value - tsint)^2 + (sint + tcost)^2 + 2 = 3+t^2 arc length = ??(3+t^2)dt are you able to end the indispensable?