Q:

Find equation of tangent at given point given x and y equations

The question asks to find an equation of the tangent line to the
curve at the given point 
x = t^2 + t
y = t^2 - t^3

Point (0,2)

I've only done questions like this where there is a given t value and not where there is an actual point given, could anyone point me in the right direction? Should I merge the x and y equations somehow?
Thanks

A:

Start by finding the value of $t$: You have $t^2 + t = 0$ and $t^2 - t^3 = 2$.
The first equation has solutions $t = 0$ (which clearly doesn't work in the second equation), and $t = -1$, which does. Hence, you just need to find the slope when $t = -1$.
Now in order to find the slope, it will be useful to know that the slope is just
$$\frac{dy/dt}{dx/dt}$$

