The manager of a weekend flea market knows from past expe-rience that if he charges $x$ dollars for a rental space at the mar-ket, then the number $y$ of spaces he can rent is given by theequation $y=200-4x$ .$\begin{array}{l}\text{ (a) Sketch a graph of this linear function. (Remember that the }\\ \text{ rental charge per space and the number of spaces rented }\\ \text{ can’t be negative quantities.) }\\ \text{ (b) What do the slope, the }y\text{ -intercept, and the }x\text{ -intercept of }\\ \text{ the graph represent? }\end{array}$

Key Concepts: Linear Functions, Graphing, Slope, Intercepts Explanation: This question is asking for a sketch of a linear function and interpretation of the slope and intercepts. Step by Step Solution: Step 1. To sketch a linear function, we need two points on the line. We can find two points on the line by setting y = 0 and finding the corresponding value of x for one point, and setting x = 0 and finding the corresponding value of y for the other point. Step 2. Setting y = 0 yields 0 = 200 - 4x, which implies x = 50. So one point on the line is (50,0). Step 3. Setting x = 0 yields y = 200 - 4(0), which implies y = 200. So the other point on the line is (0,200). Step 4. Plotting these two points and connecting them with a straight line gives us the graph of the function. Step 5. The slope of the line is -4, which represents the rate of change of the number of rental spaces with respect to the rental charge per space. As the rental charge per space increases by $1,thenumberofrentalspacesdecreasesby4.Step6.They-interceptofthelineis200,whichrepresentsthemaximalnumberofrentalspacesthemanagercanrentforfree.Thatis,ifthemanagerdoes{n}^{\prime }tchargeanyrentalfee,thenhecanrentoutall200spacesathisdisposal.Step7.Thex-interceptofthelineis50,whichrepresentstherentalchargeperspaceatwhichthemanagercanrentoutall200spaces.Thatis,ifthemanagercharges$50 per rental space, then he will rent out all 200 spaces available to him.