Let
x-------> the number of tickets
y------> the profit in dollars
Let
[tex]A(0,-400)\ B(40,0)[/tex]
Find the slope of the linear equation
The slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{0+400}{40-0}[/tex]
[tex]m=10\frac{\$}{ticket}[/tex]
the linear equation is
[tex]y=10x-400[/tex]
Statements
case A) The y-intercept represents the cost per ticket
The statement is false
The cost per ticket represent the slope of the linear equation
The y-intercept is the value of the profit for a number of tickets equal to zero
In this problem the y-intercept is the point [tex](-400,0)[/tex]
case B) The slope represents the money spent before the sale of the first ticket
The statement is False
The slope represents the cost per ticket
the money spent before the sale of the first ticket is the y-intercept
case C) The sports club must sell more than [tex]40[/tex] tickets to make a profit
The statement is True
Because
we know that
For [tex]x=40\ tickets[/tex]
the value of the function is
[tex]y=0[/tex]
in the linear equation
[tex]y=10x-400[/tex]
For [tex]x>40\ tickets[/tex]
the profit will be
[tex]y > 0[/tex] --------> see the graph
therefore
the answer is
The sports club must sell more than [tex]40[/tex] tickets to make a profit
