We need to choose the graph that can represent the relation
[tex]y=ax+b[/tex]
where y is the net profit, in dollars, a is the price of each ticket, in dollars, x is the number of sold tickets, and b is a negative constant representing the production cost, also in dollars.
Step 1
Identify the value b (the production cost, in dollars), and find the value a (the price of each ticket):
[tex]b=-1200[/tex]
Since for x = 200, they obtained y = 1200, we have:
[tex]\begin{gathered} 12000=a\cdot200-1200 \\ \\ 12000+1200=200a \\ \\ 13200=200a \\ \\ a=\frac{13200}{200} \\ \\ a=66 \end{gathered}[/tex]
Step 2
Use the previous results to find the expression for y:
[tex]y=66x-1200[/tex]
Step 3
Identify the correct graph.
Notice that y increases when x increases, so the function is increasing.
Also, for x = 0, y = -1200.
Thus, the graph of this relation is a line with a positive slope and a negative y-intercept.
Answer
Therefore, the correct graph is
