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. The variables below are defined. Write a linear equation in slope-intercept form to represent the cost to have floors carpeted.

Answer 1

To represent the total cost to have floors carpeted in your home, we can define the variables as follows:

• Let \( x \) be the number of rooms that need carpeting.
• Let \( y \) be the total cost of carpeting those rooms.

The cost includes a carpet price of $100 per room and a flat installation fee of $50.

The total cost can be expressed with the following components:

• The cost for carpeting \( x \) rooms is \( 100x \).
• The flat installation fee is $50.

Putting it all together, the total cost \( y \) can be represented by the equation:

\[ y = 100x + 50 \]

This equation is in slope-intercept form \( y = mx + b \), where:

• \( m = 100 \) (the slope, representing the cost per room)
• \( b = 50 \) (the y-intercept, representing the flat installation fee).