Problema Solution
a. Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p).
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ONE WAY TO SOLVE IT
(42,20) and (52,10)
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slope = (10-20)/(52-42) = -1
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Form: p = mx+b
You know m = -1 and y = 20 when x = 42.
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20 = -42 + b
b = 62
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Equation:
p = -x + 62
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ANOTHER WAY TO SOLVE IT WITH
MORE CLARIFICATION AND STEPS
First find the slope (referred to as m)
slope is given by the formula:
m = (y1-y2)/(x1-x2)
When p=20, x =42. This is a set of coordinates. The p is just another letter for y. So y1=20, x1=42
When p=10, x =52. This is a set of coordinates. The p is just another letter for y. So y2=10, x2=52
m=(20-10)/(42-52)
m=(10)/(-10)
m=-1
Then plug the slope and one set of coordinates into the formula. I'll pick y1 and x1
p = mx + b
20 = -1(42) + b
20 = -42 +b
62 = b
So the formula for the demand equation is p = -1x + 62 (note that -1 times something just makes the number negative, you could also show it as p = -x + 62)