SOLUTION: Please help me solve this equation: Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crow

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this equation: Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crow      Log On


   

Question 947787: Please help me solve this equation: Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less people will be willing to pay, due to the crowding and smaller lot sizes. In fact, if it builds 20 houses in this particular development, it can sell them for $640,000 each, but if it builds 70 houses, it will only be able to get $440,000 each. Obtain a linear demand equation (Let p be the price of a house and q the number of houses.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Plot +p+ on the vertical axis
Plot +q+ on the horizontal axis
------------------------------
You are given the 2 points, ( q,p ):
( 20, 64 )
( 70, 44 )
( +p+ is scaled down by +1%2F10000+ )
-------------------------------------
Use the general point-slope formula
+%28+y+-+44+%29+%2F+%28+x+-+70+%29+=+%28+64+-+44+%29+%2F+%28+20+-+70+%29+
+%28+y+-+44+%29+%2F+%28+x+-+70+%29+=+20+%2F+%28-50%29+
+%28+y+-+44+%29+%2F+%28+x+-+70+%29+=+-2%2F5+
Multiply both sides by +5%2A%28+x+-+70+%29+
+5%2A%28+y+-+44+%29+=+-2%2A%28+x+-+70+%29+
+5y+-+220+=+-2x+%2B+140+
+5y+=+-2x+%2B+360+
+y+=+-%282%2F5%29%2Ax+%2B+72+
---------------------
check:
( 20,64 )
+y+=+-%282%2F5%29%2Ax+%2B+72+
+64+=+-%282%2F5%29%2A20+%2B+72+
+64+=+-8+%2B+72+
+64+=+64+
---------------
You can check the other point
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+100%2C+-10%2C+80%2C+-%282%2F5%29%2Ax+%2B+72+%29+