The consistent ratio of 0.25 across all data points confirms the proportional relationship between x and y, indicating that any increase in x corresponds to a proportional increase in y. Here option A is correct.
In proportional relationships, the ratio between corresponding terms in two lists is always the same. This means that if we multiply or divide one term in one list by a certain number, we must do the same to the corresponding term in the other list to maintain the proportion.
Let's calculate the ratios between the corresponding terms in the table:
x y Ratio (y/x)
25.6 6.4 0.25
72.8 18.2 0.25
77.2 19.3 0.25
As you can see, all the ratios are equal to 0.25. This means that the relationship between x and y is proportional. In other words, for every increase in the value of x, there is a corresponding increase in y, maintaining a constant ratio.
This proportional relationship holds true across all data points in the given table. Here option A is correct.
Complete question:
Determine if the table shows a proportional relationship.
x 25.6 72.8 77.2
y 6.4 18.2 19.3
A - Yes, it is proportional because all y over x ratios are equivalent to one fourth.
B - Yes, it is proportional because all y over x ratios are equivalent to one third.
C - No, it is not proportional because 25.6 over 6.4 does not equal 18.2 over 72.8.
D - No, it is not proportional because 18.2 over 72.8 does not equal 77.2 over 19.3.