I dedicate some time with the nasty idea that we’re moving from one dimension to two — that one single pont that takes two numbers to find…. and that these graphs are like maps, and so the easiest way to give directions to taht “one single point that takes to numbers to find” is to give the back and forth and the up and down… two numbers, one place. (It kinda helps that our roads are a grid here ;)).
Yesterday I had a poor soul completely frustrated because she kept thinking that the second number in interval notation was “y”

Student obviously does not understand basic concepts such as point representation and slope, and/or is high and/or is grasping at the first possible method that presents itself to the student’s awareness.

Super late to the party, but… I see this most often in my students who never internalized slope as a *rate of change* as opposed to just “rise over run” = “y/x”.

I hammer into my students that slope is a rate of change: it is *change in* y over *change in* x. Every time they say rise over run, I say it back to them as change in y over change in x.