Question

At $450 per person, an airline anticipates selling 300 tickets for a particular flight. At $500 p person, the airline anticipates selling 150 tickets for the same flight. Assume a linear relation between the cost per ticket C and the number of tickets, x sold. Whi the following equations can be used to model the given information?C=-(2)/(3)x+555C=-(2)/(3)x+550C=-(1)/(3)x+555C=-(1)/(3)x+550

Answer 1

$C=-\frac{1}{3}x+550$

1) We can begin by writing C as a function of x and find the slope between two points (300,450) and (150,500)

$\begin{gathered} C=mx+b \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{500-450}{150-300}=\frac{50}{-150}=-\frac{1}{3} \end{gathered}$

2) Now that we know the slope, we need to find the linear coefficient (y-intercept), using one of those ordered pairs: (150,500)

$\begin{gathered} 500=-\frac{1}{3}(150)+b \\ -\frac{1}{3}\left(150\right)+b=500 \\ -50+b=500 \\ b=550 \end{gathered}$

So the function is:

$C=-\frac{1}{3}x+550$