Question

at 7:00 p.m. last night the temperature was 10° f at 7:00 a.m. the next morning the temperature was -2° f the temperature changed by steady amount overnight by how much did it change each hour

Answer 1

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:

$\begin{gathered} T(t)=mt+b \\ \text{where:} \\ m=\text{slope}=\text{rate of change} \\ b=y-\text{intercept} \\ so\colon \\ m=\frac{T2-T1}{t2-t1}=\frac{-2-10}{19-7}=\frac{-12}{12}=-1 \end{gathered}$

The temperature decrease by -1 ° F every hour