Finding the demand function Here is the problem: 

Suppose that an oligopolist charges a price of 500 and sells 200 units of output per day. If the oligopolist increases its price about 500, quantity demanded will decline by 4 units for every 1 increase in price. On the other hand, if the oligopolist lowers price below 500, quantity demanded will increase by only 1 unit for every 1 decrease in price. 

Here is what I did: 
point 1: (200, 500)
point 2: (196, 501)

Then find slope using m=(y2-y1)/(x2-x1) and then use point-slope form for the line. I think I am interpreting the demand increase/decrease incorrectly, but am not sure?

Thanks!
I don't have a question to "correctly interpret" , but I think the way you are calculating the demand function is correct. The demand curve in an oligopoly can be kinked (bowed out), as this one is. I think it is mathematically accurate to write the function split across the domains, as such:

$Q = \begin{cases} 
700 - P, &amp; 0  \leq P\leq 500 \\
2200 - 4P, &amp; 500&lt; P&lt; 550
\end{cases}$

where I have written quantity as a function of price, and assumed that the quantity is strictly positive.