Because you are requesting graphic design, I selected laptops that can take more graphics load over cpu load. I've avoided anything that relies on an integrated graphics card. I would recommend a SSD so that Adobe programs and files can load up quicker but that is just an added plus.
The cheapest option is an Acer Laptop Aspire:
It goes for 487$, has a NVIDIA 940MX and a i5 62000U. If you're not familiar with the intel letter system, the U means that it is a power saving core and, thus; it will have much less power that it's HQ, K, X, etc. counterparts. If you're looking for max savings this should do it, however, it comes with 8 GB of RAM so you may not be able to run too many adobe programs simultaneously without seeing a performance hit and the hard drive will likely be a bottleneck for laptop speed. If you go with this laptop you might want to consider buying a complimentary SSD to go along with it.
$487 at Newegg
The next is HP Pavilion (I've had great success with the Pavilions in the past):
It comes with a GTX 960 and a i5 6300HQ, and is a solid laptop although again, the hard drive might be a bottle neck (most laptop manufactures put nice components and a crappy hard drive in the laptop to bring down price but wow you with components). On the upside it is touchscreen, which might be a plus for art (probably not since you probably have a pressure sensitive drawing tablet if you do extensive graphic design) and the most amount of RAM of all the options at 12 GB. Be aware that the laptop is made of some crappy plastic, so the laptop may not be able to take the beating of an on the go active lifestyle banging around in a thin backpack and are notorious for splitting and cosmetic breakage. A solid option otherwise.
$780 at newegg MSRP $900
My personal favorite among the choices is the Dell Inspiron:
It comes with a i5 7300HQ and features 8GB of DDR4 RAM for faster "natural" operating speed (applications are loaded into memory). This laptop also comes with a 256 SSD which will make boot times, startup speed, and application startup absolutely glorious. Again the 8GB of RAM may get filled up if you open a lot of applications, but your SSD will be able to act as SWAP memory without slowing down your laptop extensively.
$784 at newegg MSRP $1,100
If you go with the Acer or the HP, I would recommend turning on NTFS compression so that you can shift the laptop's operating load away from the hard drive and on to the CPU since both have decent processors (especially the HP). You should not turn compression on for the Dell option, because it has an SSD (In the interest of space, I won't go into detail about that reason here).