The motherboard model you have specified, does not seem to exist. You might be talking about Gigabyte GA-H61M-S...
https://www.gigabyte.com/Motherboard/GA-H61M-S-rev-10#sp
If that is the case, then your board has...
Expansion Slots
1 x PCI Express x16 slot, running at x16
(The PCI Express x16 slot conforms to PCI Express 3.0 standard.)
* Whether PCI Express 3.0 is supported depends on CPU and graphics card compatibility.
1 x PCI Express x1 slot
(The PCI Express x1 slot conforms to PCI Express 2.0 standard.)
The 750ti will go into the PCIex16 slot, it is very much compatible.