Flooring City is running a limited time special on carpeting. The cost to have your home carpeted is $100 per room and a $50 flat fee for installation.

Question

Flooring City is running a limited time special on carpeting.  The cost to have your home carpeted is $100 per room and a $50 flat fee for installation.

Part II: Identify the 
y-intercept of the equation you wrote in Part I.  Then, state the meaning of the 
y-intercept in terms of the problem situation.

GPT-4o mini · Answer

To identify the y-intercept in this situation, let's first write the equation representing the cost of carpeting your home.

Let:

$ x $ = the number of rooms to be carpeted
$ y $ = the total cost

The total cost $ y $ can be represented by the equation:

\[ y = 100x + 50 \]

Here, $100 is the cost per room, and $50 is the flat fee for installation.

Y-intercept

In the equation $ y = 100x + 50 $, the y-intercept occurs when $ x = 0 $. To find the y-intercept:

\[ y = 100(0) + 50 \] \[ y = 50 \]

Meaning of the Y-intercept

The y-intercept of 50 means that if you have 0 rooms to carpet (i.e., you are not carpeting any rooms in your home), the total cost will still be $50. This amount represents the flat fee for installation that is charged regardless of the number of rooms being carpeted. Hence, if no carpeting is done, you still incur a cost of $50 for the installation service.