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
The rate of change is constant for a linear relationship. To find the rate of change, we can calculate the change in total cost for a 20 square foot increase.
Change in total cost: 980 - 840 = 140
Change in square feet: 140 - 120 = 20
Rate of change = Change in total cost / Change in square feet
Rate of change = 140 / 20
Rate of change = $7 per square foot
Therefore, the rate of change of the total cost in dollars with respect to the number of square feet purchased is $7 per square foot.