The thresholds for the relative poverty lines are determined in practice as a percentage q from the mean or from the median of the income population distribution. The percent q is usually considered around 50% in the case of mean and about 60% for the median. In the scientific literature is not mentioned a credible justification for choosing the proportion q. For this reason we suggested in the present work four axioms A1-A4 to be verified compulsory by the relative poverty lines. In addition, we proposed more possible income distributions X from different populations and we also proved graphically that an arbitrary variable X can or cannot satisfy the restrictions AI-A4.Having in mind this last result it is necessary in the future to improve the methodology for a more accurate selection of the poverty thresholds.
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