Welcome to DC! You can make several kinds of pasta without a pasta machine. It is easier with a pasta machine, but if you can roll dough and roll it thin, you don't need a pasta machine.
I used to roll out pasta and cut it into lasagna noodles. I finally decided that it was worth getting a pasta roller. Now I make linguine too. I use whole grain wheat flour, so I find that the spaghetti doesn't work too well.