Final answer:
The relation is quadratic because the rate of change between the x and y variables is not constant, which suggests a pattern indicative of a quadratic relationship.
Step-by-step explanation:
To determine whether the relation is linear, quadratic, or neither, we should examine the rate of change between the x and y variables. A linear equation is represented in the form y = mx + b, where m is the slope and b is the y-intercept. For a relation to be linear, it should have a constant rate of change, meaning for each unit increase in x, y should change by a fixed amount.
Looking at the given values:
- From x=0 to x=1, y decreases by 1 (45 to 44).
- From x=1 to x=2, y decreases by 3 (44 to 41).
- From x=2 to x=3, y decreases by 5 (41 to 36).
- From x=3 to x=4, y decreases by 7 (36 to 29).
The change in y is not constant but rather increases by 2 each time (1, 3, 5, 7). This pattern suggests a quadratic relationship, where the change in y is related to the square of x (quadratic term). Therefore, this relation is quadratic rather than linear or neither, as evidenced by the changing difference between consecutive y-values.