extra point, optional$)$ The streamline, pathline, and streakline for the velocity field

$2t$ at $t=0$ were obtained as the following during the lecture.

streamline:

$x=e^s$

$y=e^s$

pathline: $$

$x=y*y^{lny}$

streakline:

$x=e^{-(1+)}$

$y=e^{-}$

The figure below shows these lines for the reference point $x=1,y=1.$ The question is how the streakline

is drawn? That means, how can we transform from the streakline equations listed above to the one shown

on the plot.