Question

how does the boiling point of water change with the increase in the atmospheric pressure

Answer 1

The higher the vapour pressure of a liquid at a given temperature, the lower the normal boiling point (i.e., the boiling point at atmospheric pressure) of the liquid. The vapour pressure chart to the right has graphs of the vapour pressures versus temperatures for a variety of liquids.

Answer 2

At the higher elevations. the atmospheric pressure is lesser so the boiling water is also lesser. At this the gaseous and liquid become identical...
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