# Parametric Equation Help :)

• Nov 26th 2006, 11:49 AM
lakitu
Parametric Equation Help :)
Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

Thank you

Work out parametric equations for the straight lines through this pair of points.

(-4, 2, 0) and (-3, 3, 0).

x = y= z=
• Nov 26th 2006, 12:01 PM
topsquark
Quote:

Originally Posted by lakitu
Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

Thank you

Work out parametric equations for the straight lines through this pair of points.

(-4, 2, 0) and (-3, 3, 0).

x = y= z=

Let the parameter be t.

We want a function x(t) that gives x the values -4 and -3. Well, this is supposed to make a line, so we need to make x(t) a line. I'm going to have x(t) pass through the points (t, x) = (0, -4) and (1, -3).

$x(t) = mt + b$ where $m = \frac{-3 - -4}{1 - 0} = 1$. Now I will plug the point (0, -4) into this:
$x(t) = t + b$

$-4 = 0 + b$

$b = -4$

So my first parametric function will be $x(t) = t - 4$.

Now we need a y(t). Again we must make y(t) linear, but now we also have to pass the function y(t) through the points (t, y) = (0, 2) and (1, 3) so that it matches what x(t) does.

So $y(t) = m't + b'$ where $m' = \frac{3 - 2}{1 - 0} = 1$. We easily find that $b' = 2$, so that
$y(t) = t + 2$.

Notice that changing the parameter t does nothing to the z coordinate of the points on the line. Thus $z(t) = 0$.

So the parametric version of your line is:
(x(t), y(t), z(t)) = (t - 4, t + 2, 0).

The only difference in any other correct solution is the choice of t values I used. (Recall that I used t = 0 and t = 1.) We could easily have used $t = \pi$ and $t = \sqrt{2}$ or something. That would merely change the scale of the parameter and would still produce a correct solution.

-Dan
• Nov 26th 2006, 12:02 PM
CaptainBlack
Quote:

Originally Posted by lakitu
Hey everyone I have just been given this question as homework, but dont know where to start? any help on getting started would be great !

Thank you

Work out parametric equations for the straight lines through this pair of points.

(-4, 2, 0) and (-3, 3, 0).

x = y= z=

Given two points P and Q the line through them is L(x)=P+(Q-P)x

RonL
• Nov 26th 2006, 12:19 PM
lakitu
hey tahnk you for your reply...I dont understand what your writing though, is there anything abit easier to understand?
Thank you
• Nov 26th 2006, 12:58 PM
lakitu
I get it now thank you for your time its really appreciated :) gonna go do the rest now :)