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Homework Statement:
 Unsatisfied with the Celsius and Fahrenheit temperature scales, you decide to create your own. On your temperature scale, the ice point is 77° M and the steam point is 437° M, where M stands for "my scale." What temperature of your scale corresponds to 68°F?
Relevant Equations:

Not sure, because I think you have to make your own equations.
I found the relationship M = 2F, but got the wrong answer.
M  F  
Ice Point  77°M  32°F 
Steam Point  437°M  212°F 
437°M  77°M = 360°M
212°F  32°F = 180°F
∴ M = 2F
M = 2(68°)
M = 136°
But this is incorrect. The answer is actually 149°M. Please help.