Final answer:
To find a rule for the input-output table, we look for a pattern in the multiplication or addition of numbers. The observed pattern is that outputs are three times their corresponding inputs, with an inconsistent additional adjustment. Without a consistent adjustment, we cannot define a single rule for the table.
Step-by-step explanation:
To write a rule for the given input-output table with inputs 2, 6, 9, 10 and corresponding outputs 7, 14, 21, 23, we need to find a mathematical relationship between the input (x) and the output (y). Observing the table, we see that for the first three input values, the output is three times the input. However, for the last input (10), the output is not 30 (as would be expected if the pattern held) but rather 23. This suggests there may be an additional part of the rule that adjusts the output. Let's try to establish a pattern:
- Input: 2, Output: 7 (2 * 3 + 1 = 7)
- Input: 6, Output: 14 (6 * 3 - 4 = 14)
- Input: 9, Output: 21 (9 * 3 - 6 = 21)
- Input: 10, Output: 23 (10 * 3 - 7 = 23)
It seems that the rule involves multiplying the input by 3 and then either adding or subtracting a number to get the correct output. However, without a clear pattern in the adjustment, we cannot define a single, consistent rule based on the provided data. More information or additional data points would be needed to determine the exact rule. If the adjustment after multiplication by 3 were consistent, we could define a rule such as y = 3x + b where b is the consistent number added or subtracted. Since that's not the case, the rule remains undefined.