Variable DC offset with op amp
I am going to make two assumptions here that I suspect were implicit in the original problem statement. 


The 100K 'variable resistor' is actually a potentiometer, not just a variable resistor. 
The power supplies are actually +/-15V, not just +15


Now if you draw an inverting amplifier, Vo = -Vin you need only two equal value resistors (value to be determined but probably something in the range of 10K-1M) 

Connect one end of the potentiometer to +15 and the other end to -15. now you have a voltage source that varies from +15 to -15 as you rotate the pot, and it has a source resistance of 0\$\Omega\$ to 25K\$\Omega\$ depending on the pot rotation (maximum at mid-rotation). 

There's an implicit requirement not to have the pot response too nonlinear, so we would not want to load the pot wiper too heavily, but say 100K (say to ground or something similar) would be fine. If you loaded it with (say) 1K the last little bit of rotation on either end would do most of the work and it would be very fussy to set and probably not very stable. 

That's enough of a hint for now, see if my assumptions and the suggestions above lead anywhere for you.