Let:
T1 = Initial temperature
T2 = Final temperature
t1 = Initial time
t2 = Final time
Since the temperature changed by steady amount overnight, we can represent the temperature as a function of the time as a straight line:
[tex]\begin{gathered} T(t)=mt+b \\ \text{where:} \\ m=\text{slope}=\text{rate of change} \\ b=y-\text{intercept} \\ so\colon \\ m=\frac{T2-T1}{t2-t1}=\frac{-2-10}{19-7}=\frac{-12}{12}=-1 \end{gathered}[/tex]The temperature decrease by -1 ° F every hour
