Hey sepoto.

All they are doing is getting an equation for the tangent line to the function you started off with that goes through the origin.

They solve for the value of a and then plug that back into the equation for the tangent line and the value of a is such that it goes through the point (0,0).

That is all that equation means: its an equation for the tangent line (of form y = mx + b) that is both tangent to the function and also goes through (0,0).