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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?
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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dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.0lets start at point (1,3) what slope do you need to hit point (3,2)?

dan815
 one year ago
Best ResponseYou've already chosen the best response.0hint slope=(y2y1)/(x2x1)

dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay so this means that for 1 unit of x you have 5/4 units in y

dan815
 one year ago
Best ResponseYou've already chosen the best response.0we are start at 1,3 so we need to make sure x=1 and y=3 at starting so at t=0

dan815
 one year ago
Best ResponseYou've already chosen the best response.0<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> \[<x,y>=<1+t,3+\frac{5}{4}t> \\ =<1+t,3\frac{5}{4}t>\]

dan815
 one year ago
Best ResponseYou've already chosen the best response.0this 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.0because 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.0just 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.0but 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay that makes sense
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