Question

A company manufactures and sells video games. A survey of video game stores indicated that at a price of $88 each, the demand
would be 200 games, and at a price of $38 each, the demand would be 1,200 games. If a linear relationship between price and
demand exists, which of the following equations models the price-demand relationship?
(Let x represent the price per video game and y represent the demand.)
A
y = 20x- 1,560
В.
y = 20x
C.
y = -20x + 1,960
D.
y = -20x + 1,560

Answer 1

The price-demand relationship of the company is a linear model

The equation that models the price-demand relationship is y = -20x + 1960

How to determine the linear relationship?

From the question, we have the following points:

(x, y) = (88, 200) and (38, 1200)

The equation of the linear relationship is then calculated as:

$y = \frac{y_2 - y_1}{x_2 -x_1} * (x - x_1) + y_1$

Substitute known values in the above equation

$y = \frac{1200 - 200}{38 -88} * (x - 88) + 200$

Evaluate the difference

$y = \frac{1000}{-50} * (x - 88) + 200$

Evaluate the quotient

$y = -20 * (x - 88) + 200$

Expand

$y = -20x + 1760 + 200$

Evaluate the sum

$y = -20x + 1960$

Hence, the equation that models the price-demand relationship is y = -20x + 1960

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