Difficult# Points with Unknown Constants

SATMAT-FD4EJG

Line $ p $ is described by the equation $ 3x + 2y = 7 $, and line $ q $ is described by the equation $ y = -1.5x + 2 $.

If the point $ \left( a, b \right) $ is on line $ p $, and the point $ \left( a, c \right) $ is on the line $ q $ in the $xy$ -plane, then which of the following MUST be true?