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?

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3 Answers
Nov 18, 2017

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#.

Nov 18, 2017

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($)/(ft)^2#
So,price=200*area
for area 20,200 sq.ft
price is
#200*20200=4040000$#

Nov 18, 2017

#"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.