We want to know how the rate of change relates to a graph of the data set. Let's remind ourselves of the data we collected and the graph we made. If the measurements are made of a different size of washers, the data will likely be different.

Number of Washers	Weight
$0$	$0.07$
$1$	$0.26$
$2$	$0.45$
$3$	$0.64$
$4$	$0.83$
$5$	$1.02$
$6$	$1.21$

We then created a scatter plot of the data.

Scatter plot of the data as drawn on a calculator

The rate of change in the weight can be found by subtracting the weight between two arbitrary points and then dividing by the change in the number of washers. We can use the points

(0, 0.07)

and

(1, 0.26) .

\frac{Rise}{Run} = \frac{Change in weight}{Change in number of washers} ⇓ \frac{Rise}{Run} = \frac{0 . 2 6 - 0 . 0 7}{1 - 0} = 0.19

The rate of change is

0.19 .

To see how the rate of change relates to the graph, we need to look into the pattern the points follow.

Scatter plot of the data. A line is drawn through the points

The points lie on the dashed line. This line has a rate of change, or slope, of $0.19 .$ The rate of change shows how the function changes as we move along the $x -$ axis. In this case, a rate of change of $0.19$ means that as we add one washer to the plastic bag, the weight of the bag increases by $0.19$ pounds.

Exercise