# Calculus

I need help to start this problem please,

A company can sell 4500 pairs of sunglases monthly when the price is \$5. When the price of a pair of sunglasses is increased by 10%, the demand drops to 4250 pairs a month. Assume that the demand equation is linear.
Find the demand equation

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1. Assume the demand equation is linear.

We have two known points:

P1(5,4500), and P2(5.50,4250)

To fit a straight line between two known points, we can apply the two-point form of line, namely,
(x-x1)/(x2-x1)=(y-y1)/(y2-y1)

The equation seems long, but its symmetry makes it very easy to memorize.

Substitute x1=5,y1=4500,x2=5.5,y2=4250, we get
(x-5)/(5.50-5)=(y-4500)/(4250-4500)
-250(x-5)=0.5(y-4500)
y=-500x+7000

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