the set of all points $(e^{t},t)$, where $t$ is a real number, is the graph of $y=$

Explanation:

Step1: Let $x = e^{t}$ and $y=t$.

Given the parametric - form of points $(e^{t},t)$.

Step2: Solve for $t$ in terms of $x$.

Since $x = e^{t}$, then $t=\ln x$ (by the definition of the natural - logarithm function, if $y = e^{x}$, then $x=\ln y$).

Step3: Substitute $t$ into the $y$ - equation.

We know $y = t$, and $t=\ln x$, so $y=\ln x$.

Answer:

$y = \ln x$