How do I backup my iPhone with photos to my Time Machine device?

apoceto wrote: ... how can i back up my iphone back up in to the time machine ?

I use iCloud to synchronize my Mac Photos with my iPhone Photos. It does it automatically-- I don't have to think about it! Then when Time Machine runs on my Mac, it backs up my Photos, too.

Set up and use iCloud Photos - Apple Support

In any case, you'd have to get the pictures from your iPhone to the Mac. Time Machine works with a Mac. Some people use a cable to transfer their pictures, but that seems like trouble to me.

Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support

Time Machine works with a Mac. Do you have a Mac?