Question

question 5 (multiple choice worth 5 points) a theater manager collected data about ticket prices and attendance for an upcoming opening night. the results were used to calculate the model ŷ = - 11.91x+460.98, where x represents the selling price in dollars and ŷ represents the predicted number of tickets sold. interpret the slope of the model in the context of the problem. for every increase of one dollar, there is predicted to be an increase in ticket sales of more than 460 tickets. for every increase of one dollar, there is predicted to be a decline in ticket sales of between 11 and 12 tickets. approximately 461 tickets sell for between 11 and 12 dollars each. approximately 12 tickets sell for between 460 and 461 dollars each.

Explanation:

The model is in the form $y = mx + b$, where $m$ is the slope. Here, $m=- 11.91$. The slope represents the change in $y$ (number of tickets sold) for a unit - change in $x$ (ticket price). A negative slope means that as the ticket price ($x$) increases by 1 dollar, the number of tickets sold ($y$) is predicted to decrease. Specifically, for every increase of one dollar in the ticket price, there is predicted to be a decline in ticket sales of approximately 12 tickets (since $| - 11.91|\approx12$).

Answer:

For every increase of one dollar, there is predicted to be a decline in ticket sales of between 11 and 12 tickets.