For example, I am working on an exercise from a Calculus book that asks to find the slope of $x=f(t), y=g(t)$ at $t=2$, where
$$ \begin{align} x^2-2tx+2t^2&=4\\ 2y^3-3t^2&=4 \end{align} $$
I have already worked out the solution and found that $dy/dx|_{t=2}=0$, but I was interested in plotting the graph just for kicks and giggles. I don't think my TI Nspire can do it, or at least I don't know how. Could I use Octave or WolframAlpha somehow? Thank you.
Geogebra is your friend in this case.
Create a slider for values of $t$.
Create a list of the possible values of $x$:
listofx=Solutions(x^(2)-2 t x+2 t^(2)=4)Create a list of the possible values of $y$:
listofy=Solutions(2 y^(3)-3 t^(2)=4)Geogebra will give you as many values of $x$ and $y$ as the equations will yield and it's happy with implicit equations.
Then turn those coordinates into points using the "Element" command.
A=(Element(listofx,1),Element(listofy,1))B=(Element(listofx,2),Element(listofy,1))Create a trace of the points A and B as you adjust $t$
Teaching a lesson now, but will post image later.