What is the y-intercept of the line graphed by the equation y = -4x + 1?
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Answer:
p = -0.05x+22
Step-by-step explanation:
The general linear equation of price-demand is
(1) <em>p = mx + b </em>
<em> </em>
where x is the demand of cards in units when they are sold at x dollars.
If for every additional card they wish to sell they need to drop the price by $0.05, then
(2) p-0.05 = m(x+1)+b
To sell 360 cards they need to set the price at $4, so
(3) 4 = m.360+b
We need to find m and b.
Operating on eq. (2) we have
p-0.05 = mx+m+b
mx+b-0.05 = mx+m+b
m = -0.05
Replacing this value in (3)
4 = (-0.05)360 +b
4 = -18+b
b = 22
So, the linear equation relating price p to demand x is
p = -0.05x+22
See graph attached.
