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## anonymous one year ago Finding a parametrization for a curve given the endpoints of (-1,3) and (3,-2) using slope?

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1. dan815

okay so they want u to use a slope so, im gonna guess jut a constant slope and it is a line connecting through these points

2. dan815

lets start at point (-1,3) what slope do you need to hit point (3,-2)?

3. dan815

hint slope=(y2-y1)/(x2-x1)

4. anonymous

-5/4

5. dan815

okay so this means that for 1 unit of x you have -5/4 units in y

6. dan815

we are start at -1,3 so we need to make sure x=-1 and y=3 at starting so at t=0

7. dan815

<-1+t,3+t> <---- is a start now we have to make sure the slope condition is satisfied for 1 change in x, we have -5/4 change in y so vector in form <x,y> $<x,y>=<-1+t,3+\frac{-5}{4}t> \\ =<-1+t,3-\frac{5}{4}t>$

8. dan815

this is only 1 representation of this vector, there are multiple other ways of saying this same thing, to see if they all mean the same thing, you have to satisfy 2 things, if the direction of travel is the same (i.e same unit vector direction) and that there is a common point between the other representations

9. dan815

because what u have defined here is not just a way to get from point -1,3 to 3,-2, but depending on whatever t you pick you have defined an infinite line

10. dan815

|dw:1441069548792:dw|

11. dan815

just that saying this vector this way is a convenient form as you have the starting point at t=0 and ending point at t=1

12. dan815

but they will ask you questions like how do you get to the ending point when t=3 or some other number and starting point at different times and such

13. anonymous

okay that makes sense

14. anonymous

thank you!!

15. dan815

you're welcome

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