Parameterizing a Line: Cross Through P(3,-5) with Direction V(2,8)

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Homework Statement



Parameterize a line, L, such that is crosses through the point P=(3, -5) and direction v=(2, 8). Now, using this parametrization determine the following points belong to L: P1=(73, -180) and P2=(5, -14)

Homework Equations





The Attempt at a Solution


I really need help with this type of questions in major need of help and explanations.
 
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welcome to pf!

hi vanitymdl! welcome to pf! :smile:

let's start with the first part

can you do …
vanitymdl said:
Parameterize a line, L, such that is crosses through the point P=(3, -5) and direction v=(2, 8).
 
okay all I know is where the point is located, so with the direction is it going towards that point?
 
vanitymdl said:
okay all I know is where the point is located, so with the direction is it going towards that point?

The line L passes through the point P and has direction v, so it goes away from the point P, say, to another point Q on its path.
 
Oh so that line is going to stop at (2,8)?
 
okay I think I have an idea now
since P is (3,-5) and v (2,8)

then (x,y) = (3,-5) + t(2,8)
which is (3+2t, -5+8t)

x = 3+2t
y = -5+8t
 
Ah I'm excited I figured that out. Okay just to clarify the second part, I get my x and y then equal it to the point that I'm trying to figure out if its in the line?
 
If my t's for the x and y give me different value does that mean that they don't belong to the line?
 
For the same point, t is a constant, so it should stay the same for both x and y.