Linear demand function

Question

An office supply store has a linear demand function for binders. When the price of binders is $4, the store sells 560. When the price is $9, the store sells 260 binders. Find an equation for the demand.

Answer 1

Hi Zane,

 

A linear equation is the equation of a line.  

 

The slope-intercept form of a linear equation
(y = mx + b) tells us that we need to know two things in order to write the equation for a linear function:

    1.  Its slope (m)

    2.  Its y-intercept (b)

 

Let's begin by identifying our two given points which will determine our line, using the input price value and its corresponding output quantity value:

    1.  Point #1:  (x₁,y₁) = (4,560)

    2.  Point #2:  (x₂,y₂) = (9,260)

 

The slope (m) determined by these two points is given by the equation:

    m = (y₂ - y₁) / (x₂ - x₁)

 

Solving for slope (m) by plugging in our values for (x₁,y₁) and (x₂,y₂):

    m = (260 - 560) / (9 - 4)

    m = -300 / 5

    m = -60

 

Now to compute y-intercept (b), we can plug in our calculated slope (m) and the coordinates of one our given points into the slope-intercept form of the linear equation and solve for y-intercept (b).  We'll use our 1st given point (x₁,y₁):

   y = mx + b

   560 = (-60)(4) + b

      b = 560 + 240

      b = 800

 

Now we have everything we need to write the equation of our linear function:

      y = -60x + 800

 

If we have two given points, we can always determine the slope and y-intercept needed to write an equation to describe the line.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.