Is there an equation for the relationship between illuminance and the resistance of a light dependent resistor?
As @yhyrcanus said, I would refer to the manufacturer datasheet.

This datasheet shows the sensitivity of the photodiode as 8 ohm/lux. There's the slope of your equation.

This datasheet from Adafruit gives a little info on photoresistors and also shows the R vs lux graph on page 5.

According to the Adafruit datasheet, photoresistors can vary greatly from the same batch, &pm;50% or more. So you may want to characterize each photoresistor individually if you need a specific sensitivity.