As an extension, I challenged some students to make a spreadsheet (with formulas) that would write a function for any linear function values they put into their table.
I had a couple of boys excited about the task and it was great to see some of their misconceptions drawn out through the activity.
Misconception #1: Rate of change is always just the difference in output values
Their initial table had x values increasing by 1. When they finally got a working function I congratulated them...and then asked, "What if the x's increased by 2 and didn't start at 1?". I even changed their table values and they realized their function now didn't work in this new situation. Motivated by a new layer of challenge they went back to work.
Misconception #2: Zero term is always the term before the first term in the table
Prior to the experience they thought the zero term (connected to arithmetic sequence concept we'd been doing) was the term before the values represented in the table. For the table above that may have been for them the x = 4 or even x = 3 value rather than thinking of when x = 0.
Being nerdy and excited about spreadsheets myself I completed the challenge as well and made it a fun visual function machine. Here's the link to mine.