The table shows the total cost of different numbers of square feet of carpet. What is the rate of change of the total cost in dollars with respect to the number of square feet purchased for this linear relationship?
Number of Square Feet Purchased
120
140
160
180
Total Cost (dollars)
840
980
1,120
1,260
To find the rate of change, we need to determine the change in total cost for each additional square foot of carpet purchased.
The total cost increases by $140 when going from 120 square feet to 140 square feet: $980 - $840 = $140
The total cost increases by $140 when going from 140 square feet to 160 square feet: $1,120 - $980 = $140
The total cost increases by $140 when going from 160 square feet to 180 square feet: $1,260 - $1,120 = $140
Therefore, the rate of change of the total cost in dollars with respect to the number of square feet purchased is $140 per square foot.