The catalog store has data indicating that, when the price of a cd bookcase is $134, the demand quantity is 96 and the supply quantity is 120. the equilibrium point occurs when the price is $100 and the quantity is 112. find the linear demand equation.

A linear function has the form y = ax + b

In this case, x is the price and y is the demand.

And you can state the values of the constants a and b if you know two points.

Here you know the points (134, 96) and (100, 112).

Using (134, 96) you get 96 = 134a + b

Using (100, 112) you get 112 = 100a + b

Now you just have to solve that system of two equations.

subtract the second from the first:

112 - 96 = 100a - 134a = > -34a = 16 = a = - 16 / 34 = -8/17

And now you can find the constant b from any of the two equations of the system:

b = 112 - 100a =  112 - 100(-8/17) = 112 + 800/17 = [1904+800]/17 = 2704/17

=

The the equation if -8/17 x + 2704/17

-(8/17)x + 2704/17