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Start by writing the input column as x and the output column as y. Look for a constant difference: subtract each y value from the next one. If the differences match, the rule is likely addition or subtraction. Next, divide each change in y by the change in x. A constant ratio suggests multiplication. Test a simple rule such as y = 2x + 1 by substituting every input. Record each calculation in a small check table. If one row fails, identify whether the error came from arithmetic or from the rule itself. Try common patterns like doubling, halving, adding a fixed number, or multiplying then adding. Finally, write the rule in words and in symbols, then verify it with a value that was not given. Show each step in your homework so a teacher can follow your reasoning clearly.
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