Final answer:
After calculating the ratios of y to x for each pair of values and finding that the ratio is a constant 0.2, we can conclude that x and y have a directly proportional relationship.
Step-by-step explanation:
To determine if the variables x and y have a proportional relationship, we can compare the ratio of y to x for each pair of values. If the ratio is constant, then x and y are proportional. Looking at the provided values:
- For x=20, y=4, the ratio (y/x) is 4/20 = 0.2
- For x=25, y=5, the ratio (y/x) is 5/25 = 0.2
- For x=45, y=9, the ratio (y/x) is 9/45 = 0.2
- For x=50, y=10, the ratio (y/x) is 10/50 = 0.2
Since the ratio is the same for all pairs of values, we can conclude that x and y are directly proportional. If we were to plot these points on a graph, we would get a straight line that goes through the origin, reinforcing our conclusion of direct proportionality.