Exercise 1.2.16

Question

The manager of a weekend flea market knows from past experience that if he charges $x$ dollars for rental space at the market, then the number $y$ of spaces that will be rented is given by the equation $y = 200 - 4x.$
    \begin{enumerate}[label=(\alph*)]
        \item Sketch a graph of this linear function. (Remember that the rental charge per space and the number of spaces rented can’t be negative quantities.)
        \item What do the slope, the $y$-intercept, and the $x$-intercept of the graph represent? 
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item The graph can be sketched as follows:
    \begin{figure}[H] \centering
    \begin{tikzpicture}
    \begin{axis}[axis lines=left, xmin=0, xmax=55, ymax=210, ymin=0, xlabel={$x$}, ylabel={$y$}, x label style = {at={(ticklabel cs:0.9)},anchor=south,above=4.8mm}, y label style={anchor=north, above=3mm}]
         \addplot[domain=0:50, samples=2, mark=none, color=blue, ultra thick] {200-4*x};
    \end{axis}    
    \end{tikzpicture}
    \end{figure}

\item \begin{itemize}
    \item The slope $-4$ means that if the manager demands $1$ dollar more for a rental space, people will rent 4 spaces less.
    \item The $y$-intercept of 200 means: if the spaces were for free, people would occupy 200 spaces. This is, most probably, the overall number of spaces since the demand for spaces is usually large and everything would be occupied if they were free of charge.
    \item The $x$-intercept of 50 means: if the manager charges more than 50\$, then the spaces become too expensive for the public and no one will occupy them.
    %The slope $-4$ represents the rate of change of the charged amount of money with respect to the number of spaces. $y$-intercept represents the number of spaces when the charged money $x$ is equal to $0.$ $x$-intercept represents the amount of money $x$ when the number of spaces that will be rented is equal to zero.
    \end{itemize}
\end{enumerate}

Exercise 1.2.16

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Exercise 1.2.16

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