Question

Which of the following could be the graph of the relationship?

Answer 1

We need to choose the graph that can represent the relation

`y=ax+b`

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):

`b=-1200`

Since for x = 200, they obtained y = 1200, we have:

`\begin{gathered} 12000=a\cdot200-1200 \\ \\ 12000+1200=200a \\ \\ 13200=200a \\ \\ a=(13200)/(200) \\ \\ a=66 \end{gathered}`

Step 2

Use the previous results to find the expression for y:

`y=66x-1200`

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