So I own a Giant Boulder and currently changed its tires to some slicks and it is way different from its mountain bikes tires, the slicks are thinner, way lighter and faster. So I noticed I can go faster and wanted to know if it is possible to change the cassette to have more gears. I currently have 7 gears on the back and wanted to put maybe 8 or 9. It is possible to change the cassette or is just for road bikes. Also my shifter only goes to 7 so I need to change it also right? Also the derailleur?

Nobody knows?

I think it's technically possible to put eight of the cogs from a 9 speed cassette onto a seven speed freehub to make it an eight speed, but otherwise a seven speed freehub won't accept a normal 8+ speed cassette. And yes, in either case you would need a different shifter.

Generally speaking, you'd need a new rear wheel with an 8/9 speed hub, a new cassette, and the appropriate new shifter.

Sounds like what you need is to shift the gearing range up, rather than increasing the number of gears. What are the tooth counts of the upper and lower gears on the back, and the front? You could put bigger chainrings on the front, or smaller cogs on the back. The back is probably easier, as should not require changing the dérailleur. The front might need to change it if you did the change there.

EDIT: Oh! and is a freewheel or freehub?
https://www.sheldonbrown.com/free-k7.html

Read this -

https://www.bikeforums.net/bicycle-mechanics/571613-mysterious-world-freehub-spacing.html

The shifters determine how far the derailleur moves. Unless you have friction shifters. Any index shifter will only shift the number of times it is indexed for. Or so I have been told.

Sounds as though your problem is getting a high enough gear to give you more speed. So your 11/28 -7 speed cassette will not give you a higher gear just by adding more gears. The 11t gear is going to be the "Fastest" you can get.

But it is possible to put a larger chain ring on top give you higher gearing. Not certain what gearing you have at present- But if it is an older style you probably have 48/38/28 chainrings fitted. A trip to the LBS will confirm but it is possible to get higher gears for most chainsets.

That is true... most modern derailers that are designed for indexed systems can handle as many gears as the shifter allows.

With a friction system you can run multiple cassettes... my touring bike runs an 8 speed with friction but could just as easily run a 7 or a 9 on the same hub.

A 7 speed cassette would require a spacer to make it fit properly.

As for getting higher gears...if you are already running an 11 as a high in the rear you are maxed out and would need to run a larger chain ring up front.

You should fit a 12-28 7 sp cassette which will give you one higher gear than your present setup. https://www.sheldonbrown.com/harris/k7.html If that isnt enough you could put on a 46 tooth big chainring, which would be another gear higher. Neither of these require a total rebuild of the drive system. You would have to move the fr der up a bit for the bigger chainring.

Im currently using the biggest gear in front and the smallest gear in the back and it just seems it isnt enough.

As said here.