Welcome!
I'll assume you do not have a bunch of useless anti-virus and "cleaning" apps installed. Correct me if I'm wrong because those will make an Mac computer run like it's 1995 all over again. 😳
"Slow" with that model had nothing to do with the RAM but everything to do with the mechanical hard drives Apple installed. For 2011 and 2012 non-Retina Macbook Pros, replacing the mech drive with an SATA 6G solid-state drive (SSD) gave an 8-10X increase in data transfer speeds that made the computer feel like a much newer model.
Example: My 2012 Macbook Pro 13's original mech drive tested at 60-70MB/sec transfer speeds even when new. With an inexpensive SSD conversion I did at home, it now does nearly 500MB/sec. I've owned the computer over 11 year and it still sees daily use because it remains a pleasure to use.
👉🏻 However, prior to 2011 (including yours), the bus speed for the logic board's drive connection speed was half that (SATA 3G) of 2011 and 2012 models. An SSD conversion could do no higher than 250MB/sec in your model. That would be an improvement but not as stunning as the speed increase in the two later model of the same computer.
You can buy a compatible 500GB capacity SSD conversion kit for about US$55 before shipping. Might be worth it if you do it yourself. Not worth it IMHO if your have to pay a provider US$65-80/hour to do the conversion. It took me about an hour to put years more service into my 2012 model. All you need is a bit of common sense, patience, and the ability to follow video instructions.
If you want to gauge your comfort level with "DIY," the basic video overview of the process I used is here.
If the home conversion interests you, post back and I can give you sources and some important tips I learned in doing mine. There were a couple of things not covered in any published instructions.