Question

#13 the high school gym is capable of seating 1,500 people. for each game, the amount of money that the school brings in as revenue is a function of the number of people, n, in attendance. each ticket costs $15. what is the domain of this function?
#14
a. what is the rate of change (slope) of this graph?
b. what is the y - intercept?
c. interpret the y - intercept in context
john started with $300 in

Explanation:

Step1: Identify two points on the line

Let's assume two points on the line from the graph: (0, 300) and (12, 150).

Step2: Calculate the slope (rate of change)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=300,x_2 = 12,y_2 = 150$. So $m=\frac{150 - 300}{12-0}=\frac{- 150}{12}=- 12.5$.

Step3: Determine the y - intercept

The y - intercept is the value of y when x = 0. From the point (0, 300), the y - intercept is 300.

Step4: Interpret the y - intercept in context

Since the graph is about John's savings account and the y - axis represents the balance in the account, the y - intercept of 300 means John started with $300 in his savings account.

Step5: Find the domain of the revenue function in #13

The gym can seat 1500 people. The number of people n must be a non - negative integer and $0\leq n\leq1500$. So the domain is $\{n\in\mathbb{Z}:0\leq n\leq1500\}$.

Answer:

a. The rate of change (slope) is - 12.5.
b. The y - intercept is 300.
c. The y - intercept means John started with $300 in his savings account.
For #13, the domain of the function is $\{n\in\mathbb{Z}:0\leq n\leq1500\}$