I have been a teacher for over 20 years - all the stuff I upload has been tried and tested in my classroom. I don't mind a discussion on Twitter too where I also share new resources. I now have a personal website: https://andylutwyche.com/
This is an activity, with accompanying worksheets, that should encourage a discussion between students and teacher about equations of graphs/functions and what each part "does" regarding the position of the line/curve. You could lead on to other discussions about how the function/equation could be presented.