Algebra-1

Question Analysis
This question involves evaluating the nature of a relationship between two variables using a table of values. The main focus is on determining whether the relationship is linear or non - linear by examining the consistency of changes in y when x increases by a constant amount (3 units here).

Key Concept Explanation
A linear relationship is defined by a constant rate of change: when x increases by a fixed interval, y must increase or decrease by a constant value. This is because linear functions follow the form , where m (the slope) is constant, so  (for a fixed ,  remains the same).
A non - linear relationship lacks this constant rate of change. When x increases by a fixed interval, the changes in y () are not consistent, meaning the slope varies.

Step-by-step Solution
1. Identify the constant change in x: Here, x increases by 3 each time (from 2 to 5: ; from 5 to 8: ; from 8 to 11: ).
2. Calculate changes in y ():
From  to 

Click "Show Answer" to reveal the answer and analysis