SOLUTION: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a       Log On


   

Question 174289: 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research).
a. Suppose that 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)).
Answer by solver91311(24713) About Me  (Show Source):
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Your two points in (x,p) form are (x%5B1%5D,p%5B1%5D) = (42,20) and (x%5B2%5D,p%5B2%5D) = (52,10).

The two-point form of the equation of a line is y-y%5B1%5D=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29, except in this case you would substitute p for y.

Substitute the coordinate values into p-p%5B1%5D=%28%28p%5B2%5D-p%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29. Then do the indicated arithmetic and finally solve the equation for p to end up with your equation in slope-intercept (p=mx%2Bb) form.