Final answer:
The table given with the pairs (x, y) as x = 0, 5, 10, 15 and y = 10, 20, 40, 80 does not represent a proportional relationship because the ratios of y to x are not constant, which is required for a relationship to be proportional.
Step-by-step explanation:
The student has asked whether the table showing the pairs (x, y) as x = 0, 5, 10, 15 and y = 10, 20, 40, 80 represents a proportional relationship between x and y.
To determine if the relationship is proportional, we need to see if the ratio of y to x is constant for all pairs. Let's calculate the ratio for each pair:
- For x = 0, y = 10, the ratio is undefined since we cannot divide by zero.
- For x = 5, y = 20, the ratio is 20/5 = 4.
- For x = 10, y = 40, the ratio is 40/10 = 4.
- For x = 15, y = 80, the ratio is 80/15, which is not equal to 4.
Since the ratios are not constant, specifically the last ratio not being equal to 4, we can conclude that the given table does not show a proportional relationship between x and y. A proportional relationship would have a constant ratio, often represented by the proportionality constant k in the equation y = kx, and would result in a straight line graph passing through the origin (0, 0) on a coordinate plane.