Solving Parametric Equations to Show Line Passing Through 2 Points

[John O' Meara]

Homework Statement

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 $$(x_{0},y_{0}),(x_{1},y_{1})$$.

Homework Equations

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.

 

[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?

 

[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 $$\sqrt{x^2 +y^2}$$.

 

[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.

 

[Feldoh]

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

 

[John O' Meara]

Thanks for the replies.