Q:

A sports club is holding a fundraiser dinner. The function graphed models the profit, y, in dollars, from selling x tickets.Select True or False to describe each statement.

Accepted Solution

A:
Letx-------> the number of tickets y------> the profit in dollarsLet [tex]A(0,-400)\ B(40,0)[/tex]Find the slope of the linear equationThe 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]Statementscase A) The y-intercept represents the cost per ticketThe statement is falseThe cost per ticket  represent the slope of the linear equationThe y-intercept is the value of the profit for a number of tickets equal to zeroIn 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 ticketthe money spent before the sale of the first ticket is the y-interceptcase C) The sports club must sell more than [tex]40[/tex] tickets to make a profitThe statement is TrueBecause we know thatFor [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 graphthereforethe answer isThe sports club must sell more than [tex]40[/tex] tickets to make a profit