Question

A local cinema found that if the price of admission was $16, the attendance was about 950 customers per day. When the price of admission was dropped to $5,attendance increased to about 1550 per day. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)

Answer 1

Let the price of ticket be "p"

and attendance be "A"

First, given,

When p = 16, A = 950

Then, given,

When p = 5, A = 1550

We can model these two pairs of points as coordinates,

$\begin{gathered} (p_1,A_1)=(16,950)_{} \\ (p_2,A_2)=(5,1550) \end{gathered}$

We have to come up with the equation in the form A = mp + b, where

m is the slope and b is the y-intecept of the line.

We can use the following formula to find the equation of the line:

$A-A_1=\frac{A_2-A_1}{p_2-p_1}(p-p_1)_{}$

Let's substitute the points and find the linear equation in the form A = mp + b.

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