Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.

Question

Producers of a certain brand of refrigerator will make 1600 refrigerators available when the unit price is $420. At a unit price of $470, 5600 refrigerators will be marketed. Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.

 

p=

 

How many refrigerators will be marketed when the unit price is $520?

 

What is the lowest price at which a refrigerator will be marketed?

Answer 1

The independent variable (x) = number of refrigerators

The dependent variable (p) = unit price

 

First, know that you are given 2 points (x, p):

 

(1600, 420) and (5600, 470)

 

 

What you need to do is find the slope between these two points.  Then use the point-slope form of the line.

 

p = m(x - x₁) + p₁

 

where:

m = slope between the points

(x₁ , p₁) = any of the given points

 

I trust you know how to find the slope between any two points.

 

Since your p values increase as the x values increase, you will have a positive slope.

 

 

To find the number of refrigerators marketed at unit price of $520, use the equation to find the value of x when p=520.

 

 

The lowest price at which the refrigerator would occur when x=1.

 

 

 

If you have any questions, please let me know.