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

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

c = total cost for floors to be carpeted

r = number of rooms to be carpeted

Answer 1

To represent the cost to have floors carpeted, we start by identifying the components of the cost based on the given information:

1. The cost per room is $100. Therefore, if \( r \) is the number of rooms, the cost for carpeting \( r \) rooms is \( 100r \).
2. There is a flat installation fee of $50.

To find the total cost \( c \), we combine these two components:

\[ c = 100r + 50 \]

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

• \( m \) (the slope) is the cost per room, which is 100,
• \( b \) (the y-intercept) is the fixed installation cost, which is 50.

Therefore, the final linear equation to represent the cost to have floors carpeted is:

\[ c = 100r + 50 \]