Question

I need help to Show an equation that relates the House Price, P to the square footage, `ft^2`, and then use this equation to predict the price of a `20,200 ft^2` house?

Answer 1

Let the price of the house be `y` and the area of square footage be `x`, based on their corresponding axes.

To find the equation, we need two things - gradient and one point.

`"Gradient"=(y_1-y_2)/(x_1-x_2)`
`color(white)("Gradient")=(600000-400000)/(3000-2000)`
`color(white)("Gradient")=200`

`"Coordinates of a point on the graph" =(3000,600000)` ( can be any )

`"Equation of the graph is "y-600000=200(x-3000)`
`color(white)(xxxxxxxxxxxxxxxxxxxxxxx.)y=200x`

Hence, the price of the house is `200` times of the square footage. Therefore, a house of `20200` square footage would cost `$4040000`.

Answer 2

Price of house= 200*area (sq.ft)
I hope the line is through origin.
So u can express them using straight line equation `y=mx+c`

Explanation:

Here c=0,
`m=(deltay)/(deltax)=200000/1000=200($)/(ft)^2`
So,price=200*area
for area 20,200 sq.ft
price is
`200*20200=4040000$`

Answer 3

`"Price" = 200f`, where `f` is the square footage of the house.

Explanation:

The graph is a straight line, which means that the price is directly proportional to the area.

Use the equation of a line: `y = mx+c`

The line passes through `(0,0)`, so `c=0`

To find the slope, `m`, use the vertical change and the horizontal change.

`m = (600,000-0)/(3,000-0) = 600000/3000 = 200`

This means that the price is `$200` per `ft^2`

`"Price" = 200f`, where `f` is the square footage of the house.