The equation that models the price - sales relationship is
y = - 500x + c and the total amount of sale will be 1250.
<h3>What is Equation Modelling?</h3>
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the scenerio describing the price - sales relationship for a toy.
Assume that the linear equation is of the form -
y = mx + c
Now, suppose [x] denotes the price and [y] denotes the amount of sale.
Now at -
[x] = 6, [y] = 2000
[8] = 8, [y] = 2000 - 1000 = 1000
The coordinates through which the line passes, will be -
(6, 2000) and (8, 1000)
We know that [m] denotes the slope of the line and it can be calculated as -
m = {y(2) - y(1)} / {x(2) - x(1)}
m = (1000 - 2000)/(8 - 6)
m = - 1000/2
m = - 500
Now, the equation becomes -
y = -500x + c
Substituting point (6, 2000) in it, we get -
2000 = - 500 x 6 + c
2000 + 3000 = c
c = 5000
So, the final equation will become -
y = - 500x + 5000
If x = $7.5, the total sales would be -
y = - 500 x 7.5 + 5000 = 1250
Therefore, the equation that models the price - sales relationship is
y = - 500x + c and the total amount of sale will be 1250.
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