Respuesta :
The price of the house (y) is directly proportional to the total area of the house (x), you can express the relationship between both variables as follows:
[tex]y=kx[/tex]Where "k" is the constant of proportionality.
To determine the price of a house that has 2,000 ft², the first step is to determine the value of the constant of proportionality between both variables. For this, we have to use the known price and size of the house:
-The house has 1,500 ft² → this is the value of x
-The house costs $300,000 → this is the value of y
You can express the relationship as:
[tex]\$300000=k\cdot1500ft^2[/tex]To calculate the value of k, you have to divide both sides by 1,500ft²
[tex]\begin{gathered} \frac{\$300000}{1500ft^2}=\frac{k1500ft^2}{1500ft^2} \\ k=200\frac{\$}{ft^2} \end{gathered}[/tex]The constant of proportionality is 200$/ft², this value indicates that the price of the house increases $200 for every additional square foot.
Now that we know the value of the constant of proportionality we can calculate the price of a 2,000ft² house:
[tex]y=200\frac{\$}{ft^2}x[/tex]For x=2,000ft²
[tex]\begin{gathered} y=200\frac{\$}{ft^2}\cdot2000ft^2 \\ y=\$400000 \end{gathered}[/tex]The price of a 2,000ft² is $400,000
