Both scales are linear, so we can (mentally) draw straight lines between the data points given in the question, but we currently have two lines to think about, the Fahrenheit and Celsius. However since we are only interested in the point where they are positive and negative by the exact same amount, we can think of a single line which is the average of the two (or the sum of the two would also work), and find the point where it equals 0.

So we have 16 for the first data point and -40 for the second. If we mentally split that into seven ‘chunks’ of 8 degrees each, we can see that we want to be 2 chunks away from the point where Celsius is 0, where 7 chunks would get all the way to -40. So Celsius will be 2/7 * -40, or -80/7, which is -11 3/7 degrees. Predictably, at that point, Fahrenheit will be 11 3/7 degrees.