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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. c = total cost for floors to be carpeted. r = number of rooms to be carpeted.

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To find the linear equation for the total cost \( c \) to carpet \( r \) rooms, we need to consider both the cost per room and the flat installation fee.

  1. Cost per room: $100 per room, so for \( r \) rooms, the cost is \( 100r \).
  2. Flat installation fee: $50.

Now, we can write the total cost equation as follows:

\[ c = 100r + 50 \]

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

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

So the final equation representing the total cost to have floors carpeted is:

\[ c = 100r + 50 \]