Both scales are linear so an increase of a certain amount of energy will always result in the same amount of temperature change, regardless of the starting temperature.
As a result it’s a simple case of looking at the range over which water is liquid in the Fahrenheit scale (180: 32 – 212) and dividing by 100 from the Celsius scale to see that a change of 1°C is always the same as a change of 1.8°F. Then factor in that 0°C is the same as 32°F to get the formula:-
F = 1.8C + 32
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