A table is presented with input and output values that need to be analyzed to determine the mathematical rule governing the relationship. The table includes the following pairs: input 2 with output 18, input 5 with output 30, input 7 with output 38, and input 8 with output 42. The task is to identify which rule correctly computes the output based on the given input values. Which of the following rules is used to compute the output given the input in the table shown?

This rule suggests that the output would be nine times the input value. For input 2, this would yield an output of 18, which matches the table; however, for input 5, the output would be 45, which does not match the table's output of 30. Therefore, this rule is inconsistent with the data provided.

If we apply this rule, for input 2, the output would be 5 × 2 + 5 = 15. This does not match the table's output of 18. Similarly, for input 5, we would get 5 × 5 + 5 = 30, which matches, but the inconsistency with the first input means this rule does not hold for all pairs.

Using this rule for input 2, the output would be 6 × 2 - 6 = 6, which does not match the expected output of 18. For input 5, the output would be 6 × 5 - 6 = 24, further indicating that this rule does not fit the data in the table.