\begin{frame} \frametitle{Linear Functions: Example} \begin{exampleblock}{} When dry air moves upward it expands and cools. \begin{itemize} \pause \item ground temperature is $20\textdegree$ \pause \item temperature in height of $1$km is $10\textdegree$ \end{itemize} \pause Express the temperature as a linear function of the height $h$.\\ What is the temperature in $2.5$km height? \end{exampleblock} \pause\smallskip Since we are looking for a linear function: \begin{talign} T(h) = m h + b \end{talign} \pause We know that: \begin{talign} T(0) &= m\cdot 0 + b = 20 \mpause[1]{\quad\implies\quad b = 20}\\ \mpause[2]{T(1) }&\mpause[2]{= m\cdot 1 + b = m\cdot 1 + 20 = 10 }\mpause[3]{\quad\implies\quad m = 10-20 = 10} \end{talign} \pause\pause\pause\pause Thus $T(h) = -10m + 20$, \pause and $T(2.5) = -5\textdegree$. \end{frame}