Jan....What is the back wall...brick, wood, vinyl, etc?
If it's made of concrete, be sure to use a paint made just for that like masonry paint. Check with your local home improvement store.
If you wall is made of concrete you can paint it. Here's what we did to our concrete patio with paint:https://www.exquisitelyunremarkable.com/2018/08/how-to-paint-concrete-patio-makeover.html