Question

The quantity demanded x for a certain brand of MP3 players is 300 units when the unit price p is set at $100. The quantity demanded is 1300 units when the unit price is $50.

a) Find the demand equation.
b) Sketch its graph

Answer 1

Let x represents units of quantity demanded and y represents the unit price in dollars,

Suppose the equation that shows the relation between x and y is,

y = ax + b ( ∵ In demand equation, unit price is the linear function of quantity demanded )

Here, x = 300, y = 100,

100 = 300a + b -----(1),

If x = 1300, y = 50,

50 = 1300a + b -----(2),

Equation (1) - equation (2),

50 = -1000a

`\implies a = -(50)/(1000)=-(1)/(20)`

From equation (1),

`100 = -(1)/(20)* 300 + b\implies 100 = -15 + b\implies b = 115`

Thus, the required demand equation,

`y=-(1)/(20)x + 115`

Graphing :

Plot the points (300, 100) and (1300, 50),

Then join them by a line.

That line represents the graph of the given situation.