Question

How do I write a linear equation for the attendance in terms of the price?

Answer 1

Let:

A = Attendance

p = Price

A linear equation is given by:

$\begin{gathered} A=mp+b \\ Where\colon \\ m=slope \\ b=y-intercept \end{gathered}$

So:

$\begin{gathered} (p,A)=(17,1950) \\ 1950=17m+b_{\text{ }}(1) \\ ----------- \\ (p,A)=(14,2450) \\ 2450=14m+b_{\text{ }}(2) \end{gathered}$

Using elimination to solve the system:

$\begin{gathered} (1)-(2) \\ 1950-2450=17m-14m+b-b \\ -500=3m \\ m=-\frac{500}{3} \end{gathered}$

Replace m into (1):

$\begin{gathered} 1950=-\frac{500}{3}(17)+b \\ b=1950+\frac{8500}{3} \\ b=\frac{14350}{3} \end{gathered}$

Therefore, the linear equation is:

$A=-\frac{500}{3}x+\frac{14350}{3}$