Does the price of gasoline have an impact on the price of natural gas?

Not really. The two fuels are independent of one another. Gasoline is a refined product of crude oil, and thus directly related to the price of oil, while natural gas is produced directly from underground hydrocarbon deposits, like crude oil. Natural gas prices are dependent on the supply and demand for natural gas. In some instances, crude oil and natural gas are found in the same place and produced together. Fuel oil, like gasoline, is a refined product of crude oil and is also a substitute fuel for natural gas in some industrial facilities. In these cases, fuel oil competes with natural gas. Because oil prices are high, fuel oil does not offer much competition to natural gas and does not help to keep natural gas prices down.