11.2.1 Introduction to 3D

Investigate the figure below. Try typing different equations and ordered pairs in the input on the left. Try rotating the figure with your mouse. Can you zoom in? Zoom out?

1. Notice-Wonder

What do you notice? What do you wonder?

2. Reset the image above by clicking on the "double-arrow circle" in the top right corner.

Type (1,3,2) in the input box on the left. What happens?

3. (1,3,2)

What do you think the red line represents? Blue line? Green line? How do you know?

4. Type "2x-y+z=1" into the input line.

What do you see? What does this represent?

5. Solutions & Non-Solutions

Is (1,3,2) a solution to 2x-y+z=1? How do you know? How can you explain using the graph? How can you explain without the graph?