I hope that I understand your exercise correctly.
You could shift a log function so that it passes through the origin.
Determine the slopes of this curve at both the origin and at x = P.
Once you know these slopes, you can create lines using the Point-Slope formula.
If you're not free to choose P, m, and b, then please post all of the given information, and show us a few of the approaches that you tried in mathematica.
Cheers ~ Mark