Final answer:
The provided input-output pairs show a consistent ratio of 5 when the output is divided by the input, indicating a direct variation relationship, answer (a) Yes.
Step-by-step explanation:
When we are asked to determine if the relationship presented is an example of direct variation and given a table of inputs and corresponding outputs, we must check if the ratio of the output to the input is constant. In this case, for each input-output pair (1, 5), (2, 10), (3, 15), and (4, 20), if we divide the output by the input, we get the same constant ratio of 5. This means that the output is 5 times the input, indicating a direct variation.
For example, for the input 1, the output is 5, and for the input 2, the output is 10. This pattern continues consistently through the given pairs. Therefore, applying the definition of direct variation, characterized by the equation y = kx where k is the constant ratio, we can conclude that the relationship in this question does represent direct variation. Hence, the answer is (a) Yes.