Final answer:
Trend lines or trend curves are identified by analyzing historical data and patterns, using statistical tools and data visualization techniques to discern trends.
Step-by-step explanation:
To identify trend lines or trend curves, the correct approach is a. By analyzing historical data and patterns. This method involves collecting and organizing data, and then using statistical tools and visual representations like graphs to discern trends. The process often starts with curiosity about natural phenomena, which leads to making generalizations and developing more formal methods of data collection and analysis, as stated, "We then formulate models, theories, and laws based on the data we have collected and analyzed". Sociologists, for example, might use such methods to recognize patterns in society, as mentioned, "Seeing patterns means that a sociologist needs to be able to identify similarities in how social groups respond to social pressure". In contrast, the other options listed, such as conducting surveys and interviews (b), studying political ideologies (c), or experimenting in a laboratory setting (d), are not the primary methods for identifying trend lines in data analysis.