Dynamic Equation of the Tangent Line Problem

Hello, and thanks in advance for your help.

My math professor likes to give us problems that require a lot of synthesizing the various things we've learned recently with things we should already know. She stated this when working out the solution to this problem, but I still don't fully understand it. The problem is this:

Find the equation of the tangent line to f(x) = e^x *that passes through* the origin.

She stressed the difference between finding the tangent line to the function *at* x = 0 and finding the tangent line that passes through both x & y = 0.

Any assistance someone could give in clearing up this tricky problem would be greatly appreciated.