Caption: An air density versus Celsius temperature plot with fits to the data (see Wikipedia: Density: Air) with a degree 2 polynomial function and an exponential function.

The air density data is for a constant air pressure = 1 atm. For Earth atmosphere, see Wikipedia: Atmosphere of Earth: Composition.

Note standard atmosphere pressure = 1 atm = 101.325 kPa = 1.01325 bar = 14.696 Psi and standard temperature and pressure (STP): T =298.15 K =25 C, P=100 kPa = 14.504 psi).

The curve in the plot approximates a straight line, but this is just because the temperature range is so small on the Kelvin temperature scale: ∼ 250 to 310 K. In fact, on the Kelvin temperature scale, at constant pressure, the air density should be inversely proportional temperature to good accuracy/precision: i.e.,

  air density ρ ∼∝ 1/T  . 

That this is so is because air to good accuracy/precision obeys the ideal gas law P = (N/V)kT which implies that

  density ρ ∝ particle density N/V 
            ∝ 1/(Kelvin temperature T) 

Credit/Permission: © User:T.seppelt, 2017 / CC BY-SA 4.0.
Image link: Wikimedia Commons: File:Air density vs temperature.svg.
Local file: local link: air_density.html.
File: Earth atmosphere file: air_density.html.