Answer
To express the revenue from a baseball game, R as a function of the ticket price during the year, we use:
\[R\left( x \right)=mx+b\].
Work Step by Step
Consider the provided statement “A baseball team plays in a large stadium and with a ticket price of $\$15$ , the average attendance at recent games has been $20,000$. A market survey indicates that for each $\$1$ increase in the ticket price, attendance decreases by $400$.”
With a ticket price of $\$15$, the average attendance at recent games has been $20,000$ and the market survey indicates that for each $\$1$ increase in the ticket price, attendance decreases by $400$. Suppose x is the revenue from a baseball game. Then the revenue from a baseball game will be x times the number of spectators at a baseball game -- that is, $26,000-400x$.
$\begin{align}
& R\left( x \right)=\left( 26,000-400x \right)x \\
& =26,000x-400{{x}^{2}} \\
& =-400{{x}^{2}}+26,000x
\end{align}$
The linear function representing the number of spectators at a baseball game will be of the form $R\left( x \right)=mx+b$
