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?

Answer 1

To find the rate of change of the total cost in dollars with respect to the number of square feet purchased, we can look at the table provided.

Number of Square Feet (x) | Total Cost (y)
100 | $500
200 | $1000

To find the rate of change, we need to first calculate the slope of the line passing through the two points (100, $500) and (200, $1000).

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = ($1000 - $500) / (200 - 100)
Slope (m) = $500 / 100
Slope (m) = $5

Therefore, the rate of change of the total cost in dollars with respect to the number of square feet purchased for this linear relationship is $5 per square foot.