Question

A company manufactures and sells video games. A survey of video game stores indicated that at a price of $66 each, the demand would be 400 games, and at a price of $36 each, the demand would be 1,300 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.)

Answer 1

Answer:

$y=-30x+2380$

Step-by-step explanation:

$x\rightarrow$ represent price per video game.

$y\rightarrow$ represent demand.

The linear equation in slope intercept form can be represented as:

$y=mx+b$

where $m$ is slope of line or rate of change of demand of game per dollar change in price and $b$ is the y-intercept or initial price of game.

We can construct two points using the data given.

When price was $66 each demand was 400. $(66,400)$

When price was $36 each demand was 1300. $(36,1300)$

Using the points we can find slope $m$ of line.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{1300-400}{36-66)}$

$m=\frac{900}{-30}$

$m=-30$

Using point slope form of linear equation to write the equation using a given point.

$y-y_1=m(x-x_1)$

Using point $(66,400)$.

$y-400=-30(x-66)$

⇒ $y-400=-30x+1980$    [Using distribution]

Adding 400 to both sides:

⇒ $y-400+400=-30x+1980+400$

⇒$y=-30x+2380$

The linear relationship between price and demand can be written as:

$y=-30x+2380$