Question

chain find the rate of change of the function by using two points from the table.
feet of chain purchased | cost (dollars)
5 | 13.75
10 | 27.50
15 | 41.25
the rate is select choice
this means that each foot of chain costs $ select choice

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(\frac{y_2 - y_1}{x_2 - x_1}\).
Let's take two points from the table, say \((5, 13.75)\) and \((10, 27.50)\). Here, \(x_1 = 5\), \(y_1 = 13.75\), \(x_2 = 10\), \(y_2 = 27.50\).

Step2: Calculate the rate of change

Substitute the values into the formula: \(\frac{27.50 - 13.75}{10 - 5}=\frac{13.75}{5} = 2.75\).
We can check with another pair, like \((10, 27.50)\) and \((15, 41.25)\): \(\frac{41.25 - 27.50}{15 - 10}=\frac{13.75}{5}=2.75\). So the rate of change is \(2.75\) dollars per foot. This means each foot of chain costs \(\$2.75\).

Answer:

The rate is \(2.75\) dollars per foot. This means that each foot of chain costs \(\$2.75\).