Answer
The required equation is $N(P)=\dfrac{-50}{3}P+\dfrac{2000}{3}$ number of tickets when price is $P$ dollars per ticket.
The decrease in number of tickets $\Delta N =\dfrac{-250}{3}\approx -83.33$. Here, a negative sign indicates a decrease.
Work Step by Step
Let the required function be $N(P)=m\cdot P + b$. Since, $N(10)=500$ and $N(40)=0$, so, we get $500=10m+b$ and $0=40m+b$.
Subtracting the equations gives $500=-30m$, or, $m=\dfrac{-50}{3}$.
Substitute the value of $m$ in second equation, to get $0=40\cdot \dfrac{-50}{3}+b$ , or, $b=\dfrac{2000}{3}$.
Therefore, the required equation is $N(P)=\dfrac{-50}{3}P+\dfrac{2000}{3}$.
The slope of the linear function is $\dfrac{\Delta N}{\Delta P}=\dfrac{-50}{3}$. When $\Delta P= 5$ dollars, then, $\dfrac{\Delta N}{5}=\dfrac{-50}{3} \Rightarrow \Delta N=-\dfrac{250}{3}$. Negative sign indicates decrease.
