The two key pieces of information required for this question are:
- "when the unit price is
per toaster, then the weekly demand is
toasters"
- "for every
decrease in the unit price, the weekly demand increases by
toasters"
from which it is clear that the unit price
and the weekly demand
are linearly related.
Using the 'slope-point' form of the equation of a line and considering
as a function of
, we can write
![{\displaystyle q-q_{0}=m(p-p_{0}),}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/1ab2be5f77d5482f78f52f44d6a5d6f954578cee)
where
is a 'coordinate' consisting of a price and the demand at that price, and
is the slope of the line in the
-plane.
Hence we can take
and
(when
decreases by 2,
increases by 10). Thus
![{\displaystyle {\begin{aligned}q-{\color {OliveGreen}20}&={\frac {\color {PineGreen}10}{-{\color {WildStrawberry}2}}}(p-{\color {OrangeRed}16})\\q&={\color {blue}-5(p-16)+20}\,.\end{aligned}}}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/2877766c6db719681d32cb9b821051a9bb8e9991)
Note: Considering
as a function of
is equally correct and leads to the equivalent answer