This document provides instructions for using a graphing calculator to explore linear inequalities and integer addition visually. It guides the user to create sliders and points on a number line to represent linear expressions and the addition of integers. Adjusting the sliders allows observation of how changing the variables affects the linear inequality and integer sum. The final construction enhances understanding through an interactive visualization of these mathematical concepts.

1. Graphing Calculator

2. Contents
Linear Inequalities
Visualizing Integer Addition

3. Linear Inequalities
Task
Graph a linear inequality ax + b ≤ c that can be explored using
sliders.

4. Enter ax + b ≤ c into
the Input Bar and
press Enter.
Hint: You can use the
Virtual Keyboard to
enter the ≤ symbol.
GeoGebra will
automatically create
sliders for the
parameters a, b, and c

5. Use the Move tool to
adjust the slider
values so that a = 1, b
= 1, and c = 3.

6. Change the increment
of the sliders to 1.
Hints: Select number
a and open the Style
Bar of the Graphics
View.
Style Bar
Select number a

7. .
Slider tab
Increment
Open the Settings of
number a and select
tab Slider.
Set the Increment to 1
and repeat for
numbers b and c
Settings

8. Drag the background
of the Graphics View
to move the origin to
the center

9. Zoom Out to make a
bigger part of the
coordinate system
visible on screen
Zoom out

10. Set the distance
between the marks on
the axes to 1.
Hints: Make sure that no
object is selected before
you open the Style Bar
of the Graphics View.
Open the Settings of the
axes.
Select tab xAxis and set
the Distance to 1.
Repeat on tab yAxis.
Make sure no object is selected
Change Distance

11. Finally, you can select
all objects and
animate. What do you
observe?

12. Visualizing Integer Addition
Task
Create a dynamic figure that visualizes the
addition of integers on the number line.

13. Open the Settings of
the Graphics
View using the Style
Bar

14. On tab xAxis set the
distance of tick marks
to 1 by checking the
box Distance and
entering 1 into the
text field.
Change Distance

15. On tab Basic set the
minimum of the xAxis
to -11 and the
maximum to 11
Set here

16. On tab yAxis uncheck
Show yAxis and close
the Settings.
Uncheck Show yAxis

17. Create two sliders a
and b, both
with Interval -5 to 5
and Increment 1
Sliders a and b

18. Show the value of the
sliders instead of their
names using the Style
Bar
Change here

19. Create points A = (0 ,
1) and B = A + (a , 0).
Hint: The distance of
point B to point A is
determined by slider a
Points A and B

20. Create a vector
u = Vector(A, B) which
has the length a
Vector u

21. Create points
C = B + (0, 1) and
D = C + (b, 0)
Points C and D

22. Create vector
v = Vector(C, D) which
has the length b
Vector v

23. Create point
R = (x(D), 0).
Hint: The
input x(D) gives you
the x-coordinate of
point D. Thus,
point R shows the
result of the addition
on the number line
Point R

24. Create point
Z = (0, 0)
Point Z

25. Create three
segments
c = Segment(Z, A),
d= Segment(B, C),
and
e = Segment(D, R)
Segments

26. Use the Style Bar to
enhance your
construction (e.g.
match the color of
sliders and vectors,
change line style, fix
sliders, hide labels and
points).

27. END
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