Question

Barbara wants to buy carpeting for her new home. She will need different sized carpets in each room.
There is a linear relationship between the size of a carpet, in square feet, and its cost.
Describe the rate of change for this relationship.
The cost of a carpet
by
per square foot.

Answer 1

In a linear relationship between the size of a carpet and its cost, the rate of change is the cost per square foot of carpet. This means that for each additional square foot of carpet, there is a corresponding increase in cost by a constant amount.

If we denote the cost of a carpet by \( C \) and the size of the carpet in square feet by \( S \), then the relationship can be expressed as:

\[ C = mS + b \]

Here:
- \( m \) represents the rate of change (cost per square foot),
- \( b \) is the fixed cost (which could represent setup or other related fees, depending on the context), and
- \( S \) is the size of the carpet in square feet.

So, if, for example, the cost per square foot is \( x \), we can say:

**The rate of change for this relationship is \( x \) dollars per square foot.**

This means for every square foot of carpet Barbara purchases, she will pay \( x \) additional dollars.