# Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

I'm not sure what this problem is asking for, I tried taking the derivative of each component, then plugging in t, but the answer gives small equations for each component like x = 1-t. I'm not sure how to reach this answer component. Can someone please explain the entire process clearly? thanks, the other online solutions seem confusing.

Well, one simple parametrization is $\textbf{r}(t_0) + t \textbf{r}'(t_0)$ where $t \in \mathbb{R}$. Convince yourself by using vector geometry with this picture in mind,