A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for \$45.

Let y represent the net profit (in dollars) when they have sold x tickets.
Which of the following information about the graph of the relationship is given?

Answer options:

A. Slope and x-intercept
B. Slope and y-intercept
C. Slope and a point that is not an intercept.
D. X-intercept and y-intercept.
E. Y-intercept and a point that is not an intercept.
F. Two points that are not intercepts.

The given information about the relationship is as follows:

D. X-intercept and y-intercept.

Explanation:

The x-intercept is the point where the graph intersects the x-axis. In this case, the x-intercept represents the number of tickets they need to sell to cover the necessary production costs. It is given that they need to sell 18 tickets to cover the costs. Therefore, the x-intercept is 18.

The y-intercept is the point where the graph intersects the y-axis. In this case, the y-intercept represents the net profit when they have not sold any tickets. It is not explicitly given, but since the organization needs to cover the necessary production costs, the net profit would be zero when they have not sold any tickets. Therefore, the y-intercept is 0.

Hence, the given information provides the x-intercept (18) and the y-intercept (0), which corresponds to option D. X-intercept and y-intercept.

To determine the answer, let's first understand the given information.

The charity organization sold each ticket for $45. This means that the revenue from selling x tickets is given by the equation: revenue = 45x.

To cover their necessary production costs, they needed to sell 18 tickets. This implies that the production costs are $18 * $45 = $810.

The net profit (y) can be calculated by subtracting the production costs from the revenue: y = revenue - production costs = 45x - 810.

Now, let's analyze the given answer options:

A. Slope and x-intercept: The x-intercept represents the point where the graph intersects the x-axis (the number of tickets required to break even). However, the x-intercept is not given in the information provided. Hence, option A is not correct.

B. Slope and y-intercept: The y-intercept represents the point where the graph intersects the y-axis (the net profit when no tickets are sold). In this case, the y-intercept is -810 (as the charity incurs a loss until enough tickets are sold to cover production costs). Thus, option B is correct as it provides the slope (45) and the y-intercept.

C. Slope and a point that is not an intercept: The point given is the required number of tickets to cover production costs, which is the x-intercept. As mentioned earlier, this information is not provided. Therefore, option C is not correct.

D. X-intercept and y-intercept: We already analyzed the x-intercept (number of tickets required to break even) and the y-intercept (net profit when no tickets are sold). Hence, option D is not correct since it does not provide the slope.

E. Y-intercept and a point that is not an intercept: We have examined the y-intercept, which is the net profit when no tickets are sold. However, the given information does not provide any additional points. Therefore, option E is not correct.

F. Two points that are not intercepts: The given information does not specify any additional points except the y-intercept and x-intercept (which fall under options B and D). Hence, option F is not correct.

Therefore, the correct answer is option B: Slope and y-intercept.

the profit is zero when they have sold 18 tickets.

So, (18,0) is on the line
The profit is 45x-18*45 on x tickets
y = 45x - 810
See what you can do with that.