My iMac running Yosemite has started slowing down my cable modem connected devises completely

Reinstalling OS X Without Erasing the Drive

Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Reinstalling OS X Without Erasing the Drive

Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the Macintosh HD entry from the the left side list. Click on the First Aid tab, then click on the Repair Disk button. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit Disk Utility and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Continue button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

Alternatively, see:

Reinstall OS X Without Erasing the Drive

Choose the version you have installed now:

OS X Yosemite- Reinstall OS X

OS X Mavericks- Reinstall OS X

OS X Mountain Lion- Reinstall OS X

OS X Lion- Reinstall Mac OS X

Note: You will need an active Internet connection. I suggest using Ethernet

if possible because it is three times faster than wireless.

If you have AppleCare, call them. Let them deal w/it.

It should not touch your data, but it never hurts to backup first.

I thought of this after posting, but have you simply tried quitting all running applications/utilities that use your local network or Internet? This problem may just be due to a problematic application. You may want to check the Console in the Utilities folder to see if it reveals anything relevant.

Most often BitTorrent, iCloud, Dropbox, or some other cloud-data application is involved in cases of mysterious bandwidth use by a Mac. If you use iCloud, uncheck at least iCloud Drive in its preference pane and see whether there's any change. If you use third-party network backup or file-sync software, disable that. If you use a torrent client, remove it.

Otherwise, if you're running OS X 10.9 or later, you can see which processes are most active on the network.

Launch the Activity Monitor application in any of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad and start typing the name.

Select All Processes from the View menu, if not already selected, and also select the Network tab.

Click the heading of the Sent Bytes column in the process table to sort the entries by bandwidth usage. You may have to click it twice to get the highest value at the top. What is it, and what is the process? Repeat with the Rcvd Bytes column.

Did you happen to start using the new Photos application and activate iCloud Photo Library? If so, your Mac will be trying to upload all the photos in your main photo library, which can saturate the upload side of your link and drag down the responsiveness of the downlink side (due to delays in acknowledging received packets). Depending on how many photos you have in your main library, this can take days. You can pause the upload for a day in Photos > Preferences > iCloud so you can get some other work done, then resume it when the Mac would otherwise be idle.