To find the equation of a line passing through the point $(3, -2)$, we need either a second point or additional information, such as the slope. Since only one point is given, I’ll assume you meant to find the equation of a line with a specific condition (e.g., slope or parallelism). Can you clarify, or do you want to explore various possibilities (like finding the equation if the slope were given)?

Let me know if you'd like to provide more information for the most accurate equation, and I'll happily create a sketch for it as well! Feel free to upload any additional info!