Q: Can I delete pictures from Photos (MacBook) and keep them in iCloud?

You have two options:

1. Enable "Optimise Mac Storage". Then Photos will only keep optimised versions of the photos on your mac and the originals in iCloud.
2. Or move your Photos Library to an external drive and delete the library from your Mac.  When you want to access the photos you will either have to connect the external drive with the library or use the web interface at www.cloud.com.

What you cannot do, however, is to delete some of the photos and keep them in iCloud.  Deleting photos from the library will delete them from iCloud and all devices.

You can set the iCloud Photo Library preferences to optimize the photos that are stored on the devices and it will keep the full version in the cloud and have smaller, optimized versions on your hard drive or mobile device.

The following is from this Apple document:

Can I use iCloud Photo Library to save space on my device?iCloud Photo Library automatically keeps all your photos and videos in the original, high-resolution version. Follow these steps to choose how you store your photos and videos on your device:

• In iOS, tap Settings > iCloud > Photos or Settings > Photos & Camera, then select a storage setting.
• In OS X, click Photos > Preferences > iCloud, then select a storage setting.

If you turn on Optimize [device] Storage, iCloud Photo Library will automatically manage the size of your library on your device, so you can make the most of your device's storage and access more photos than ever. All of your original, full-resolution photos and videos are stored in iCloud while device-size versions are kept on your device. You can download the original photos and videos over Wi-Fi or cellular when you need them.

However, you can't delete a photos from your Photos library and keep it in the iCloud Photo Library.

You can get a small portable HD, formatted OS X Extended (journaled) with ownership set to be ignored, put the library there and run it from there.

So, in option #2, if the library is deleted from my macbook, you're saying I can still access the photos on iCloud.com?

Yes, if you copy it to an external drive and still have an iCloud Photo Library on your Mac all photos can be accessed from the web interface.  Use the Photos.app at https://www.icloud.com

You can browse photos, upload photos and download photos, but not edit them. For editing, you need to connect the external drive and launch Photos on your Mac.

but how do I make sure that I have an iCloud photo library on my mac?

No problem    Don't sign out of iCloud Photo Library on your Mac in your System Preferences > iCloud > Photos > Options.

As long as this is active, your photos will stay in iCloud.

1. Wait, until your library completely has been uploaded to icloud. Check the Photos > Preferences > iCloud, if there is any progress bar indicating an upload, that is still in progress.
2. Copy the Photos Library from your Pictures folder to your external drive as described by Old Toad.
3. Double-click the copied library to open it in Photos. 
4. Now open the Photos > Preferences > General and enable the copied library as your System Photo Library.
5. Open the  Photos > Preferences > iCloud and enable the copied library as your iCloud Photo Library.

Check the copied library thoroughly - look at all Moments if it appear to be complete, try to edit photos.

Make a current backup of your Mac, and then you can delete the Photos library from your internal drive,

I'm assuming this means I do. I'm still confused though why everything won't delete off iCloud if I delete everything from Photos.

It will depend on how you delete. And as long as you a not quite clear about this, don't delete anything.

And don't delete before you have a backup copy of your Photos library.

• If you delete photo from your Photos library using Photos, the photos will be deleted from iCloud and all devices syncing with icloud.
• If you switchPhotos  to a different Photos library, for example on a different drive, the photos will stay in iCloud.

I'm also trying to save storage on my MBAir. My storage is full and I need to free up some space. I now use the iCloud Photo Library to sync all of my devices including an iMac, MBair, iPhone, and iPad. When I first moved from iPhoto to Photos my iPhoto library remained on my MBair drive and Photos created a separate library which, as I understand it, points to the original iPhoto library. The iPhoto library is 40GB and the Photos library is 10GB. I only use Photos rather than iPhoto. Can I delete both the iPhoto library and the Photos library in order to recover 50GB without losing the photos in iCloud and the other devices?

I only use Photos rather than iPhoto. Can I delete both the iPhoto library and the Photos library in order to recover 50GB without losing the photos in iCloud and the other devices?

Yes you can but you won't recover the full 50 GB.  It'll be more like 5-10 GB. Why?  This Apple document explains why: Photos saves disk space by sharing images with your iPhoto or Aperture libraries - Apple Support.

Yes you can but you won't recover the full 50 GB.  It'll be more like 5-10 GB. Why?  This Apple document explains why: Photos saves disk space by sharing images with your iPhoto or Aperture libraries - Apple Support.

Thanks OT. I've read the document but I'm confused about how the smaller Photos library and the larger iPhoto library connect or interact. The document is unclear about that. I had thought that the smaller Photos library was created to point the Photos app to the original photos in the iPhoto library where they reside. If that's not what's going on then what is?

I compared the photo libraries on the MBair to the libraries on my iMac. The iMac came with Photos so there is only a Photos library on it created from the sync with iCloud and that library is now 72GB. That's why I thought that the two libraries on the MBair interacted somehow because the conversion from iPhoto created those two libraries in contrast to the iMac Photos setup.

So just to be clear if I delete the two libraries on the MBair I would also not lose any of the photos currently in iCloud and syncing with the iMac, iPhone, and iPad?

BTW, I have my iCloud preferences on the Photos app on the iMac set to download originals to the Mac as I have a lot of storage on the iMac. As I understand it this means that I have the original photos stored both on the iMac and in iCloud. Is that correct?

I've read the document but I'm confused about how the smaller Photos library and the larger iPhoto library connect or interact. The document is unclear about that. I had thought that the smaller Photos library was created to point the Photos app to the original photos in the iPhoto library where they reside. If that's not what's going on then what is?

When you migrate an iPhoto Library to Photos the two libraries don't interact and they are not connected, but still they are sharing blocks on the disk. It is the magic of hard links as opposed to aliases or symbolic links.

Photos does not point to originals and previews in the iPhoto library. The migration creates new original files and new previews by creating a hard links to the files in the iPhoto library. These hard linked files are independent files, the same size as the originals, and you can delete and modify them independently of each other. But they are saving space because they are sharing the same entry in the file table. So the blocks on the disk are not duplicated. MacOS will count how many  hard links exist to this entry. If you delete either the original iPhoto file or the  Photos file the counter will be decremented. The space will not be released, until the counter is zero and no longer any hard link exists.