If you want to go from Celsius to Fahrenheit you use the C = 9/5 F + 32 while F = 5/9(C-32). These work ok until you ask students at what temperature are both Celsius and Fahrenheit the same.
This is when I promptly lose them because they don't realize they can determine the answer in one of two ways. They can either set the two formulas to be equal or they can graph.
As you can see if you replace the C or F with x and y, you can graph the two linear equations and they cross at the point (-40, -40). This means when the Celsius temperature is -40, the Fahrenheit is -40 and vice versa. I got the idea the other day as I was looking at the formulas and realized the formulas are basically linear and I could easily create a visual representation using Desmos. You see the results in the photo above.
The other way is to set them equal to each other and solve:
9/5 x + 32 = 5/9(x-32)
9/5 x + 32 = 5/9 x - 160/9
9/5 x + 288/9 = 5/9 - 160/9
9/5 x = 5/9 x - 448/9
9/5 x - 5/9 x = -448/9
81/45 x - 25/45 x = -448/9
56/45 x = -448/9
56 x = -2240
x = -40
This means the value has to be -40 for the two temperatures to be equal.
You could have done each equation separately by subbing x in so it looks this way
x = 9/5 x + 32
-4/5 x = 32
x = -40
or
x = 5/9( x - 32)
x = 5/9 x - 160/9
-4/9 x = -160/9
(-9/4) (-4/9x) = -160/9 * -9/4
x = -40
So there you have it. -40 Celsius is -40 Fahrenheit and a way to prove it. Have a great day and enjoy yourselves. Let me know what you think, I'd love to hear.
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