parametric equations for a line: pre-calculus

[dawnsybella]

I am so lost. I think mostly I don't understand the language. The question is:

Find a set of parametric equations for the line through P = (1, 1) and Q = (2, 4) so that P = (x(0), y(0)) and Q = (x(1), y(1))

Am I wrong to start with P and Q as line y - 1 = 3(x - 1) and then t = x - 1 and x = t + 1...? So then y = 3t + 1 and x = t + 1...?

I don't understand what "P = (x(0), y(0)) and Q = (x(1), y(1))" means.

 

[stapel]

Have parametric equations not been covered in class...?

The variables x and y are meant to be parametrized -- defined in a particular way in terms of a another variable -- so that x(0) = 1, x(1) = 2, y(0) = 1, and y(1) = 4. This is what they meant by the part you asked about.

Eliz.

 

[dawnsybella]

actually, i am in a correspondence course...and have no class time..have to pretty much figure it out on my own..this is the first time i have done anything with this kind of thing and am very confused...the book doesnt cover this type of question at all..this is the last lesson in my course..

 

[galactus]

You're on the right track.

Suppose you were to find parametric equations for the line through

\(\displaystyle \L\\(x_{0},y_{0})\;\ and\;\ (x_{1},y_{1})\)

The line is parallel to the vector:

\(\displaystyle \L\\<x_{1}-x_{0},\;\ y_{1}-y_{0}>\)

so, \(\displaystyle \L\\x=x_{0}+(x_{1}-x_{0})t,\;\ y=y_{0}+(y_{1}-y_{0})t\)