Expert: Sherry Wallin - 1/9/2011

Question
I have this algebra question from my algebra class and can not figure it out.  It is a demand equation which I always seem to get lost in. Do you think you could help me so that I may be able to get the other parts of the question?Here it is.
 Suppose a market research company finds taht at a price of p=$20, thye would sell x=42 tiles each month.  If they lower the price to p=$10 then more people would purchase the tile, and the can expect to see x=52 tiles in a month.  Find the equation of the line for hte deamnd equation written in the form of p=mx+b.

I do not know how to find m or b.

Answer
Hi, these problems are usually linear equations and usually you are given enough information, like data fro two points that you can use to find the slope (m) of the equation that describes the demand equation. Here you are given p = 20 and x = 42 which equates to an ordered pair of (42, 20). I case yo don't know normally price is on the vertical axis (y-axis) and quantities are on the horizontal (x-axis). Next you are given that p = 10 and x = 52 so the 'other' ordered pair is (52,10). Now use the formula for slope: (y2-y1)/(x2-x1) = (20-10)/(42-52) = 10/-10 = -1. The negative slope indicates that as the price per tile goes down the number of tiles sold goes up (or vice versa). So the only thing left that you need to do is write your demand equation in the form of y = mx + b which is really p = mx + b. I would use the point slope form of the line to go there: y-y1 = m(x-x1) or in your case -> (p-p1) = -1(x-x1)-> p-10 = -1x+ 52 -> p = -x + 52  + 10 -> p = -x + 62. You can always check that both the points you used are on this line:

20 ?= (-1)42 + 62. Is 20 =? 20? Yes this point works. Check the other one out too: 10 ?= -1(52) + 62, i.e., is 10 ?=10? Yes, so you may rest assured that your demand equation does describe the data you were given.

Math Prof