Science:Math Exam Resources/Courses/MATH104/December 2015/Question 08 (a)/Solution 1

The two key pieces of information required for this question are:

• "when the unit price is $\mathrm{\$}16$ per toaster, then the weekly demand is $20$ toasters"
• "for every $\mathrm{\$}2$ decrease in the unit price, the weekly demand increases by $10$ toasters"

from which it is clear that the unit price $p$ and the weekly demand $q$ are linearly related.

Using the 'slope-point' form of the equation of a line and considering $q$ as a function of $p$, we can write

$q-q_0=m(p-p_0),$

where $(p_0,q_0)$ is a 'coordinate' consisting of a price and the demand at that price, and $m$ is the slope of the line in the $pq$-plane.

Hence we can take $(p_0,q_0)=(16,20)$ and $m=\frac{10}{-2}$ (when $p$ decreases by 2, $q$ increases by 10). Thus

$\begin{array}{rl}q-20& =\frac{10}{-2}(p-16)\\ q& =-5(p-16)+20.\end{array}$

Note: Considering $p$ as a function of $q$ is equally correct and leads to the equivalent answer $p=-\frac{q}{5}+20.$