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 of the total cost with respect to the number of square feet purchased, we need to calculate the slope of the line that represents the relationship between the two variables.
Using the points (120, 840) and (140, 980) to calculate the slope:
Slope = (980 - 840) / (140 - 120) = 140 / 20 = 7
Therefore, the rate of change of the total cost with respect to the number of square feet purchased is $7 per square foot.