First, we can write the linear equation we are trying to find as,

C = mF + b,

where C is the dependent variable (the measure we are converting to) and F is the independent variable (the measure we are converting from).

Second, we can find the equation to convert from °F to °C using the information provided. Specifically, we know both the boiling point and freezing point of water in °F and °C.

We can find the slope of the line, m, using the two points that we know to lie on the line,

(F₁,C₁) = (32, 0),

(F₂,C₂) = (212, 100).

Using these points we find m as,

where the equation of our line can now be written as,

To find the C-intercept (y-intercept) of the line, b, we can use either point lying on the line as follows,

which imply that,

Thus, to convert temperatures in °F to °C, you would use the equation,

Close window