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

`y=-30x+2380`

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=(y_2-y_1)/(x_2-x_1)`

`m=(1300-400)/(36-66))`

`m=(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`