Q: How do I deleted my photos on my phone but keep them in iCloud

Howdy barbarafromodessa,

I understand the desire to free up space on your iPhone by keeping your pictures elswhere and removing them from your phone.

If you are not using iCloud Photo Library you can sync the pictures to your computer and select which pictures get synced back to your phone.

See:

Sync your iPhone, iPad, and iPod with iTunes using USB - Apple Support

and:

Sync photos from your computer to your iOS device using iTunes - Apple Support

Note however, if you have iCloud Photo Library enabled it handles the sharing of pictures between devices keeping them in the cloud and making them available on all devices.

To save space on your iPhone with iCloud Photo Library enable you can set it to optimize storage.

iCloud Photo Library FAQ - Apple Support

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:

• On your iPhone, iPad, or iPod touch, tap Settings > iCloud > Photos or Settings > Photos & Camera, then select a storage setting.
• On your Mac, 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. 

If you turn on Download Originals, iCloud Photo Library will keep your original, full-resolution photos and videos in iCloud and on your device. Download Originals is the default setting for iOS devices with the free 5 GB storage plan and for all Mac devices.

Note you still want to keep backups of your photos on your computer or elsewhere.

For information on deleting photos, see Get help with your iCloud Photo Library - Apple Support

Take care.