Question

there is a linear relationship between the size of a carpet, in square feet, and its cost. describe the rate of change for this relationship.

Explanation:

Step1: Select two points on the line

Let's take two points, say (100, 900) and (140, 1100).

Step2: Use the slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 100,y_1=900,x_2 = 140,y_2 = 1100$. Then $m=\frac{1100 - 900}{140 - 100}$.

Step3: Calculate the slope

$\frac{1100 - 900}{140 - 100}=\frac{200}{40}=5$.

Answer:

The rate of change is $5$ dollars per square foot. This means that for every additional square - foot of carpet, the cost increases by $5$ dollars.