Calculating tangent line at $t=2$ 
Calculate the tangent line at $t=2$ of the curve
  $$x(t)=t^2+2t+4,\ y(t)=1+te^t$$

How would you go about determining this? So far I have
$$x'(t)=2t + 2\\
y'(t) = te^t+e^t$$
Where do I go from here to get the tangent line?

Hint:
A directing vector of the tangent to the curve at the point $M_2$ with coordinates$(x(2),y(2))$ is the vector
$$\vec v=(x'(2),y'(2)),$$
hence a point $M(x,y)$ is on this tangent line if and only if the vectors $\overrightarrow{M_2M}$ and $\vec v$ are collinear, i.e. the determinant of their coordinates is $0$.
