Thread: Cartesan equation to parametric and vector form

Please check and please explain if it is incorrect, even if it is correct. have a very vague understanding of it. Thank you.

Convert the following Cartesan equation to parametric and vector form
3x-5y=9
y=-9/5+3/5x
y=-6/5 + 3/5(x-1)
y=-6/5+3/5t
t=x-1

x=t+1
y=-6/5+3/5t
How to write it in a vector form?
Thank you

Here is one way.
The the points are on the line. (You can pick any two.)
Therefore, the vector they determine, , directs the line.
So the parametric form is

Plato,

thank you and I have questions. Why vector is <5,3>, and not <-5, -3>
If we select two points (3,0) and (-2,-3), then v=<-2-3, -3-0>=<-5,-3>
the vector form is -5i-3j
I know it is wrong because your answer is different, but why?

Originally Posted by oceanmd

Why vector is <5,3>, and not <-5, -3>

Don't you understand that both are the same direction of that line?
They are negatives of each other, therefore parallel.
The vectors are also direction vectors of that line.
Any vector parallel to is a direction vector of the line.

Plato,
got you. Thanks.
As for the parametric form, is it a rule that if a vector is let say <7,5>, then parametric form is x=7t+5 and y=5t ?

Thank you