Step 1: Understanding the budget line.
The budget line shows the combinations of two goods that a consumer can afford given their income and the prices of the goods. The slope of the budget line is given by the ratio of the prices of the goods, which is \(-P_2/P_1\), where \(P_1\) is the price of the first good and \(P_2\) is the price of the second good.
Step 2: Conclusion.
Thus, the correct answer is option (1) \(-P_2/P_1\).