They discovered this after making a table of values. We used graphing calculators to graph the table of values and then graph the rule. I'm writing the steps up for my own reference and for students to access later.

First off, press STAT, then press Edit...

Here you will see a screen with 3 columns labeled L1, L2, and L3.

L1 represents your x values, and L2 represents your y values. Enter in a list of points, in this case it was (1,9) (2, 15) (3, 21)

When you press GRAPH in the top right, you'll get 3 points.

For some students, no points showed up. I troubleshooted this problem and found out that you need to press "2nd" "STAT PLOT" (where the Y= button is) and make sure that your Plot 1 is on so that the L1 and L2 values show up.

They seem to form a straight line if they were connected. Since there is no such thing as a Figure 1.5, this is called a

__discrete__graph. The points are separate and are not meant to be connected.

We then pressed the Y= button in the top right and entered in the rule, 6x+3. When you graph that, it connects those previously unconnected points, forming a

__continuous__graph.

I will add a picture of student work to give some context to the problem.