when you breathe the diaphragm makes your lungs expand. the expansion causes the pressure inside your lungs to be lower than outside your body. since fluid (air) goes from high to low to air flows into your lungs.
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Blood pressure by itself won't affect breathing. Breathing is regulated by the level of carbon dioxide in your blood (more specifically, carbon dioxide creates carboxylic acid in your blood and this pH decrease causes you to breath) unless you've suffered trauma to the brain. Blood pressure may indirectly cause carbon dioxide levels to raise due to increased metabolic demands of the body to maintain the higher blood pressure
When air pressure is Low it becomes very difficult to breath simply because air moves from high partial pressure to low partial pressure.