Question

2.The table below shows the relationship between the number of tickets sold for a concert and a theater's net profit, in dollars. Determine the rate of change and what the rate of change
represents in this situation.
Concert Profit
Tickets Net Profit
Sold
($)
150
-500
200
0
225
250
400 2,000
The rate of change is 1/10. This means every 1 ticket sold produces a net profit of $10.00.
The rate of change can not be determined from the table above.
The rate of change is 10. This means every 1 ticket sold produces a net profit of $10.00
The rate of change is 10. This means every 10 tickets sold produces a net profit of $1.00.

Answer 1

The true statement about the rate of change of the table is (c) The rate of change is 10. This means every 1 ticket sold produces a net profit of $10.00

How to determine the rate of change

From the table, we have the following ordered pairs

(x,y) = (150,-500) and (200,0)

The rate (r) is then calculated as:

$r = \frac{y_2 -y_1}{x_2 -x_1}$

So, the equation becomes

$r = \frac{0 + 500}{200 - 150}$

Evaluate the difference and the sum

$r = \frac{500}{50}$

Evaluate the quotient

$r = 10$

The value of the rate represents that for every 1 ticket sold, there is a net profit of $10

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