We present an analysis of the distribution of 77 supernovae (SNe) Ia relative to spiral arms of their Sab-Scd host galaxies, using our original measurements of the SN distances from the nearby arms, and study their light-curve decline rates ({Delta}m_15_). For the galaxies with prominent spiral arms, we show that the {Delta}m_15_ values of SNe Ia, which are located on the arms, are typically smaller (slower declining) than those of interarm SNe Ia (faster declining). We demonstrate that the SN Ia distances from the spiral arms and their galactocentric radii are correlated: before and after the average corotation radius, SNe Ia are located near the inner and outer edges (shock fronts) of spiral arms, respectively. For the first time, we find a significant correlation between the {Delta}m_15_ values and SN distances from the shock fronts of the arms (progenitor birthplace), which is explained in the frameworks of sub-Chandrasekhar-mass white dwarf explosion models and density wave theory, where, respectively, the {Delta}m_15_ parameter and SN distance from the shock front are appropriate progenitor population age (lifetime) indicators.