Math Help - Demand Equation Question

1. Demand Equation Question

Suppose that 10,000 units of a certain item are sold per day by the entire industry at a price of $150 per item, and that 8000 units can be sold per day by the same industry at a price of$200 per item. Find the demand equation for in terms of , the number of units sold, assuming the demand curve to be a straight line.

I know the answer will be a straight line, so P(x)=ax+b

and I know

if you sell 10000 units, price becomes $150 so in price equation above you get 150=a(10000)+b and if you sell 8000 units, price becomes$200 so the equation becomes 200=a(8000)+b

I just can't figure out how to solve to get A and B pretty much...

2. Originally Posted by redraider717
Suppose that 10,000 units of a certain item are sold per day by the entire industry at a price of $150 per item, and that 8000 units can be sold per day by the same industry at a price of$200 per item. Find the demand equation for in terms of , the number of units sold, assuming the demand curve to be a straight line.

I know the answer will be a straight line, so P(x)=ax+b

and I know

if you sell 10000 units, price becomes $150 so in price equation above you get 150=a(10000)+b and if you sell 8000 units, price becomes$200 so the equation becomes 200=a(8000)+b

I just can't figure out how to solve to get A and B pretty much...
these are simultaneous equations

$150 = 10000a + b$ ..................(1)
$200 = 8000a + b$ ....................(2)

$\Rightarrow -50 = 2000a$ ....................(1) - (2)

now solve for a. when finished, plug the value you got for a into either of the original equations to solve for b