If this is a photo synced from your computer to your phone you delete it by connecting your phone to your computer, going to the Photos tab of your iTunes sync settings, unchecking the folder that contains the photos you no longer want on your phone and syncing. (If you only want to delete a single photo, remove it from the folder and sync.)
Hi Jordan, sorry to hear you're having trouble deleting photos. You can only delete photos on your iPhone that were taken on your iPhone (i.e. they appear in Camera Roll), or photos from your iCloud Photo Stream.
To delete photos synced from your computer to your phone:
(1) With your iPhone plugged into your computer, open iTunes
(2) Select your iPhone in the sidebar on the left
(3) Click on the Photos tab. Uncheck events and albums that you don't wish to have on your iPhone.
Hope this helps!