The pK_a value of Benzoic acid is 4.19, whereas pK_a of 4–methoxybenzoic acid is

 4–methoxybenzoic acid has high pK_a value means it is less acidic because methoxy group is electron donating group that increases the electron density on ring and when the compound gives its acidic hydrogen, then the negative charge on oxygen is not properly delocalized on the ring as the ring already has high electron density. This, in turn, conjugate base has low stability.