Question 261713
They are asking you to write your answer in the form p = m*x + b.


If I take that literally, then at a price of 20, the equation would become:


20 = m*x + b


this kind of says that the price per tile is a function of the number of tiles sold per month which doesn't make a hell of a lot of sense, because it usually is that the number of tiles sold per month is a function of the price per tile.


I would think the formula should be:


42 = m*x + b where x is the cost per tile.


you would then get:


42 = m*20 + b, and you would also get:


52 = m*10 + b.


now the number of tiles sold per month is dependent on the price per tile which I believe is what you are looking for.


I can see why you are confused.


I am too.


If you are looking at a demand equation, then you want to find the demand based on the price.


I will assume my interpretation is correct and work it that way and see where it goes.


let's assume, the equation is:


d = m*p + b


this means demand = slope of the line times the price per unit + b, where b is the demand if the price is 0.


That doesn't make a hell of a lot of sense, but these straight line equations are usually only valid in a limited range of the domain so we can use it even if there are logical consistencies involved at the extremes.


our equation is:


d = m*p + b


our coordinate points are:


(p1,d1) = (20,42)
(p2,d2) = (10,52)


we find the slope (m) by the formula (d2-d1)/(p2-p1) = (52-42)/(10-20) = 10/-10 = -1.


our equation becomes:


d = -1*p + b


we substitute one of the points on the line to find b.


take (p2,d2) = (10,52)


equation becomes:


52 = -1*10 + b which becomes 52 = -10 + b which becomes 62 = b after you add 10 to both sides of that equation.


our equation becomes:


d = -p + 62


when p = 0, then d = 62
when p = 10, then d = 52
when p = 20, then d = 42


we let y = d and x = p so we can graph this equation.


equation becomes:


y = -x + 62


graph of the equation is shown below:


{{{graph (600,600,-10,90,-10,90,-x+62)}}}


this is your demand equation.


it is estimating the demand based on the price.


y values are the demand.


x values are the price.


as the price goes up, the demand goes down.


as the price goes down, the demand goes up.


they threw you a curve when they said use the equation in the form of p = m*x+b and when they showed you that p = 20.


this means that p is the price per unit and the equation is not a demand equation but a price equation which is making the price dependent on the demand rather than the demand dependent on the price.


I think that what you are looking for is the demand equation which means that the demand is dependent on the price, so the equation I gave you is accurate.


If the price were dependent on the demand, then that would be a price equation which is not what I think you are looking for.