Great question actually. The good news is that you may already have the saved view. Normally, we create a saved view first then use that saved view to create the line chart. So if you've already created a saved view when you first built that line chart, you're all done!
What you'll want to do is create a saved view that will generate the chart in the new UX. OR, alternatively, you can create a custom view in the New UX. There are plusses and minuses of each but for charts, I find that if it is a one off chart, meaning it wont' be used anywhere else, I prefer to use a custom view. The choice is yours or you might try both and see which you prefer.
For grids, I'm 50/50. Sometimes the saved view is a better option because you can easily change it classic and have that change immediately show up in the New UX.