# Parametric equations

1. Aug 17, 2009

### John O' Meara

1. The problem statement, all variables and given/known data
Show (by eliminating the parameter) that the equations,$$x=x_{0}+(x_{1}-x_{0})t$$, $$y=y_{0}+(y_{1}-y_{0})t$$, represent the line passing through the points $$(x_{0},y_{0}),(x_{1},y_{1})$$.

2. Relevant equations

3. The attempt at a solution
I get $$t=\frac{x-x_{0}}{x_{1}-x_{0}}=\frac{y-y_{0}}{y_{1}-y_{0}}$$. And further I then get $$y=mx-mx_{0}+y_{0}$$, where, $$m=\frac{y_{1}-y_{0}}{x_{1}-x_{0}}$$. I feel that this is not the answer to the question but if it isn't, I do not know what is? Thanks.

2. Aug 17, 2009

### Feldoh

Perhaps writing:

$$y=mx-mx_{0}+y_{0}$$ as $$y-y_0 = m(x-x_0)$$, $$m = \frac{y_1-y_0}{x_1-x_0}$$ rings a bell?

Last edited: Aug 17, 2009
3. Aug 17, 2009

### John O' Meara

I am sure it should but it is not ringing any bell with me. It is a while since I did coordinate geometry. And it got nothing to do with distance; the distance formula is $$\sqrt{x^2 +y^2}$$.

4. Aug 18, 2009

### RTW69

You have answered the question. Review the defination of the equation of a line through two points. You will see that with a little basic algebra your expression for t= can be rewritten in the form of that defination.

5. Aug 18, 2009

### Feldoh

Look up point-slope form (I think that's what it's called...) and I think that you'll see it ;)

6. Aug 18, 2009

### John O' Meara

Thanks for the replies.

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