How does an increase in temperature affect air pressure (in terms of weather effects)?

I've always been taught that hotter air = less dense air = lower pressure, but looking at the baretric equation (P = P_0 e-mgh/kT), it looks like higher temps lead to higher pressures….. what am I missing?

(To be clear, I'm trying to understand two adjacent outdoor regions with different temperatures – which will have higher pressure and have wind flow from it? The colder region or the hotter region)

submitted by /u/egbertian413
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