How to test the statistical significance of the difference between two Linear Regression slopes?

There are two time-series: T1 and T2. They come from different studies and mean different things. On T1 we do a Linear Regression and get the coefficient B1. On T2 we do a Linear Regression and get the coefficient B2.

- For comparison of the slopes, do I need the dependent variable to be the same?

- Can time be this dependent variable?

- What are the recommended statistical tests to apply in this case? T-test?

Thank you for your time!