Final answer:
The provided table and the additional example points do not show a consistent ratio between x and y values, indicating a non-proportional relationship. The absence of a straight line through the origin in their graphical representation also supports this conclusion.
Step-by-step explanation:
When determining whether a table represents a non-proportional or proportional relationship, we look for a consistent rate of change between the x and y values. Proportional relationships have a constant ratio, meaning that the y value is always a multiple of the x value. The original question does not provide a table that matches the typical characteristics of a proportional relationship since the y values (1, 2, 3, 4, 5) do not increase by the same factor when x values (-4, -2, 0, 2, 4) increase.
Using the example data provided (1,5), (2,10), (3,7), and (4,14), if we attempt to find the ratio of y to x, we get 5/1, 10/2, 7/3, and 14/4, which are not equal to each other. This indicates a non-proportional relationship. Additionally, if we were to plot these points on a graph, the lack of a straight line through the origin (0,0) also points to a non-proportional relationship since a proportional relationship would display a straight line passing through the origin.