Question

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.

Answer 1

the first 2 are false and the last one is true.

Explanation:

I took the test :)

Answer 2

Let

x-------> the number of tickets

y------> the profit in dollars

Let

`A(0,-400)\ B(40,0)`

Find the slope of the linear equation

The slope is equal to

`m=(y2-y1)/(x2-x1)`

substitute

`m=(0+400)/(40-0)`

`m=10(\$)/(ticket)`

the linear equation is

`y=10x-400`

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
`(-400,0)`

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
`40` tickets to make a profit

The statement is True

Because

we know that

For
`x=40\ tickets`

the value of the function is

`y=0`

in the linear equation

`y=10x-400`

For
`x>40\ tickets`

the profit will be

`y > 0` --------> see the graph

therefore

the answer is

The sports club must sell more than
`40` tickets to make a profit