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. 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 $100 $200 $300 $400 $500 $600 $700 $800 $900 $1,000 $1,100 $1,200 $1,300 $1,400 $1,500 x y Carpet size (square feet) Cost ($) Describe the rate of change for this relationship. The cost of a carpet increases increases decreases by $0.20 $1.50 $8.33 $10.00 $150.00 $200.00 per square foot.

Answer 1

To determine the rate of change for the relationship between the size of the carpet (in square feet) and its cost (in dollars), we can analyze the data provided.

The data shows a linear relationship between carpet size (x) and cost (y). To find the rate of change (also known as the slope) of this linear relationship, we can use two points from the data.

For example, using the points (100, $500) and (200, $1000):

1. **Calculate the change in cost** (Δy) and the change in size** (Δx):
- Δy = $1000 - $500 = $500
- Δx = 200 - 100 = 100 square feet

2. **Calculate the rate of change**:
\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{500}{100} = 5 \, \text{dollars per square foot}
\]

You can check this with other pairs of points in the data; they should yield the same rate of change.

Thus, the cost of a carpet increases by **$5.00 per square foot**.