Say, I have the line in $R^3$ defined by the parametric equations, $x=t$, $y=0$, and $z=t$. How would I draw this line in 2-d, using the x and z coordinate axis? I'm just brushing up a bit on my calculus 3.
Attempt: To graph it, I think I should just pick different values of t starting from 0 (or can I pick negative values) and see what values x and z takes on. Thus, it would look just like the straight line going through the origin, the same as the line y=x in the x-y plane. Am I correct?
You certainly, are correct as $x=t$ and $z=t$ for any parameter t that clearly means that it will give a line z=x as far as z-x plane is concerned .