How do I convert the rectangular equation x+y = 1 to parametric equations?

[ƒ(x)]

Convert x+y = 1 to parametric equations.

I know that z = v, but after that I'm stuck.

 

[Char. Limit]

Wait, z=v? What's that got to do with anything?

A simple way to do this is let x=t.

 

[ƒ(x)]

I need to convert it into three parametric equations for x, y, and z

 

[ZioX]

There are lots of parametrizations.

Which one you would want to use depends on what you want to do with it.

 

[ƒ(x)]

It's in the section of my book dealing with finding surface area by using double integrals.

 

[ƒ(x)]

its the infinite amount of parametrizations that throws me

 

[ZioX]

You typically pick one that cancels out factors in your integration.

 

[ƒ(x)]

ok, but my book wanted me to do it a certain way.

like when the function was x^2 + y^2 = 1

z = V
x = cosU
y = sinU

and then for another one they wanted

z = V
x = sinUcosV
y = sinUsinV

 

[ZioX]

Right, because they come out nice.

The point is that the parametization doesn't matter. The double integral will always evaluate to the same value.

(t,1-t,z) will probably work fine for you.