Exercise 1.2.17

Question

The relationship between the Fahrenheit $F$ and Celsius $C$ temperature scales is given by the linear function $F = \frac{9}{5}C+ 32.$\begin{enumerate}[label=(\alph*)]
        \item Sketch a graph of this function.
        \item What is the slope of the graph and what does it represent? What is the $F$-intercept and what does it represent?
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item The graph looks as follows:
    \begin{figure}[H] \centering
    \begin{tikzpicture}
    \begin{axis}[axis lines=left, xmin=0, xmax=55, ymax=140, ymin=0, ytick={0,32,50,100}, xlabel={$F$}, ylabel={$C$}, x label style = {at={(ticklabel cs:0.9)},anchor=south,above=10mm}, y label style={anchor=north, above=3mm}]
         \addplot[domain=0:50, samples=2, mark=none, color=blue, ultra thick] {(9/5)*x+32};
         \addplot[mark=*, mark options={scale=1, fill=blue}](0,32);
         \addplot[mark=*, mark options={scale=1, fill=blue}](30,86);
         \addplot +[dashed,gray,mark=none] coordinates {(30,0) (30,86)};
    \end{axis}    
    \end{tikzpicture}
    \end{figure}

\item The slope of the graph of the function $T$ is $\dfrac{9}{5}.$ It represents the rate of change of the temperature in Fahrenheit with respect to the temperature in Celsius. The $F$-intercept of $32$ represents the temperature in Fahrenheit when the temperature in Celsius is equal to zero.
\end{enumerate}

Exercise 1.2.17

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Exercise 1.2.17

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