If the graph of $e^y$ against $x^2$ is a straight line with gradient $3$ and it passes through the point $(1,2)$ express $y$ in terms of $x$

Question

Can someone please explain how this question is solved?

If the graph of $e^y$ against $x^2$ is a straight line with gradient $3$ and it passes through the point $(1,2)$ express $y$ in terms of $x$

Thanks in advance!

Answer 1

Let the straight line represent the relationship between $Y$ and $X$ where these capital letter symbols are the transformed variables.

Given that this line has slope $3$ and passes through $(1,2)$ can you find $Y$ in terms of $X$?

Now in that equation you got, just put $Y = e^y$ and $X = x^2$ and take logs of both sides to find $y$ in terms of $x$.