Question

The manager of a weekend flea market knows from past experience that if he charges dollars for rental space at the flea market, then the number of spaces he can rent is given by the equation\({\bf{y = 200 - 4x}}{\bf{.}}\)

(a) 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.)

(b) What do the slope, the y-intercept, and the x-intercept of the graph represent?

Short answer

1. The graph of the function on the interval is\(\left( {0,50} \right)\).
2. The result in no spaces rented.

Step-by-step solution

Given data

The number of spaces that can be rented is given by the equation:

\(y = 200 - 4x.\)

(a) Determine the graph of this linear function \(\)\(\)

Since\(x > 0\)so we can take values of\(x\)from 0 onwards and since\(y > 0\)

Therefore,

\(\begin{array}{c}200 - 4x > 0\\4x < 200\\x < 50\end{array}\)

So, we graph the function on the interval\(\left( {0,50} \right)\)

The graph is given below

The graph the given linear function is given as;

(b) Determine the y-intercept, and the x-intercept of the graph

The slope of the graph is -4, which means that for each increase of 1 dollar for rental space, the number of space rentals decreases by 4.

The y-intercept is 200, which is the number of spaces when no charges for each space.

The x-intercept is 50, and this is the smallest rental charge that results in no spaces rented.