Northern Applachia: Here's my thoughts for you...
Join HSLDA for about $100. They will give you legal covering, teaching support and answer any of your questions.
Find another homeschooling family to help figure out the nuances of homeschooling in your location.
Figure out what style learner your brother is ie. projects vs. test, oral vs. written, better in am or pm?, can sit or prefers hanging off the couch or citing the facts while running around the yard or trampoline, Can read for hours or prefers the comics, easily writes or struggles to write or even has difficulty physically writing or getting the words from his head to the page, How are his study skills? How are his job skills? How is his executive functioning skills? All of this will help you figure out how he functions best and enable you to get more from him with less time. Will he willingly allow you to teach him? Or is he willing to be responsible and learn while you direct what's next. He should be an independent learner if he is in 9-10th (or higher!) grades.
Lastly see if you have a community college that allows dual enrollment and investigate that. Some students truly do sooo much better in that type of environment that a high school one. He can then get high school and college credit.
Hope this helps and this brings you both closer.