Home construction In a proposal to prospective clients, a...

Home construction In a proposal to prospective clients, a contractor listed the following costs:\ 1. Fees, permits, site preparation 14,000 dollars 2. Construction, per square foot 95 dollars a. Write a linear function the clients can use to determine the cost $C$ of building a house having $f$ square feet. b. Find the cost to build a $2,600$ -square-foot house.

Home construction In a proposal to prospective clients, a contractor listed the following costs:\
1. Fees, permits, site preparation 14,000 dollars
2. Construction, per square foot 95 dollars
a. Write a linear function the clients can use to determine the cost $C$ of building a house having $f$ square feet.
b. Find the cost to build a $2,600$ -square-foot house.

Key Concepts

Linear Functions

A linear function represents a relationship where the change in the output is proportional to the change in the input, typically expressed in the form y = mx + b. This type of function is used to model situations where there is a fixed starting value and a constant rate of change, making it a natural choice for problems involving a constant base cost plus an additional cost proportional to a variable, such as square footage in construction.

Slope

The slope in a linear function indicates the rate of change of the output with respect to the input. In contexts like construction cost estimation, the slope represents the variable cost per unit, meaning that for every additional unit of square footage, the cost increases by a fixed amount.

Y-intercept

The Y-intercept of a linear function is the constant term that represents the starting value when the input is zero. In the context of construction, this intercept is used to model fixed costs that are incurred regardless of the size of the construction, such as fees, permits, and site preparation.

Function Evaluation

Function evaluation involves substituting a specific value of the independent variable into the linear function to calculate the corresponding output. This process is used to determine specific costs, such as the total cost for a house of a given square footage, by replacing the variable in the function with the known quantity.

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