inflation and unemployment are two intricately linked concepts, there are two possible explanations of these concepts, one in the short run and another in the long run, in the short term the inverse relationship between inflation and unemployment does exist i.e when inflation is on the higher side unemployment is on the lower side and vice versa. if u see any short term Philips curve u can see this relationship as a declining curve.
In the long run however the economists had not find any significant relationship between the two, so if u see any long term Philips curve u will see a vertical line meaning that the it is not elastic.