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Question

In a proposal for some clients, a housing contractor listed that there is a initial fee of $12,000 and a construction cost of $95 per square foot of home space. Write a linear function that can be used to calculate the cost of building a home with
x square feet of space. Next, explain why you think this is a function. Finally, use the function to estimate the cost of the construction for a 1,950 square foot home.

Answer 1

Let the cost of building a home be represented by C.

Therefore, 

 

C = 95x + 12000 is a linear function that can be used to calculate the cost of building a home.

 

It is a function because every number of square feet provided is matched by exactly one cost value. If you graph this function, you will obtain a straight line graph with a y-intercept of $12,000 and a slope of 95. Every straight line graph passes the vertical line test, which is a test to determine if a relation is a function.

 

For x = 1,950 the cost is calculated as:

 

C = 95(1950) + 12,000

 

C = $197,250