Compare 2 or more lines

Do they have the same intercept (one line) or different intercepts (different parallel lines)?
Parametric Approach: Analysis of Covariance. See chapter 11.
Nonparametric Approach. A rank-sum test on residuals from a Theil-Sen line of Y vs. X. See chapter 12.

Do the lines have the same slope? (Are they parallel?)
Parametric Approach: Analysis of Covariance. See chapter 11
Nonparametric Approach. Do confidence intervals on the Sen slope overlap? See chapter 10.

Chapter references are to the course textbook Statistical Methods in Water Resources.