How are inflation and unemployment linked?

The Phillips curve shows the relationship between unemployment and inflation. On the y axis is inflation increasing and on the x-axis is the unemployment rate increasing. The theory behind the relationship shows a line that is convex to the origin (curves away from the origin) with high inflation meaning low unemployment and vice versa. This relationship is explained by in times of high demand in the economy, firms will be employing more workers. If you think about the labour market diagram, high demand for labour would mean there would also be higher wages due to firms needed to pay more to attract the lessening amount of available labour. Therefore, wages will rise causing cost-push inflation as it means that firms' cost of production are relatively more expensive. You could also think about the relationship through inflation. For example, inflation occurs in times of economic growth (high AD) this means that firms will want to increase production thus, requiring more labour: reducing unemployment.
In the exam it is useful to evaluate your points, so it is helpful to know that this inverse relationship between inflation and unemployment doesn't always hold true. For example, in the 1970s in the UK there was a period known as stagflation (times of low/stagnant economic growth but also high inflation and high unemployment) which demonstrates that the Phillips curve isn't always correct. Removing ceteris paribus it can be said that external factors in the economy ( e.g. in the 1970s there were high oil prices) leads to the distortion of the theorised relationship between inflation and unemployment.