I've got a nasty crack in my kids' slide ( see image ).
I think the slide is plastic and I'm sure the crack will only grow if used.
Is there a way to repair this?
Replace it. The integrity is now compromised. Do not risk child safety over cheap plastic.
No adhesive, epoxy, resin or anything like that will return the original strength of the slide and any ideas involving screwing backing plates in sound good, but once you start drilling holes or screwing through things you are going to weaken the slide in multiple areas to try to save another and risk making it worse.
It may be disappointing for your child and they may have to wait before you can replace it but that's better than a trip to A and E.
Can I get an Amen?
Sorry about your slide, it looks like a good one too.