This document provides instructions on how to create dynamic figures in GeoGebra that show the solution to a system of linear equations and how to graph the derivative of a function. It demonstrates how to insert dynamic text linked to objects, construct two lines defined by sliders, find their intersection point, and display the coordinates. It also shows how to trace the slope of a tangent line to a function as its point of tangency is moved.

2. Contents
System of Linear Equations
Graphing Derivatives

3. How to insert dynamic text
Dynamic text contains an
element that refers to one
of the objects used in the
construction. Thus, the text
adapts to changes of the
object (e.g. new
coordinates, area).
Select the Text tool and click
in the Graphics View. Click
on Advanced and select tab
Objects. From the list of
available objects, select the
object which value should
be displayed in
the Graphics View.

4. How to insert dynamic text
Hint: You may also add
static parts to your
text. The dynamic part
of your text will
change, if the
construction is
modified
Static Part
Dynamic Part

5. System of Linear Equations
Task
• Create a dynamic figure that visualizes the solution of a
system of linear equations.
• Note: Such a dynamic figure can also be used to
visualize... the solution of a system of functions.
• An equation in one variable by entering each side of the
equation as one of the two functions.

6. How to insert dynamic
text
Enter the linear
equation line1:
y = m x + b into the Input
Bar.
Hint: The input line1
gives you line1.
GeoGebra will
automatically create
sliders for the variables
m1 and b1 when pressing
Enter

7. How to insert dynamic
text
Show the sliders in the
Graphics View by
clicking on the
disabled Visibility
buttons next to their
entry in the Algebra
View.
Visibility buttons
Sliders visible in Graphics View

8. How to insert dynamic
text
Repeat the same steps
for the equation of
line2: y = m_2 x + b_2.

9. How to insert dynamic
text
Let Equation1 be
rewritten as y= -2x+1
and Press Enter and
Equation2 as y=1x-1
and Press Enter.
Use the Style Bar to
change the color of
both lines and their
sliders

10. How to insert dynamic
text
Use the Text tool to
create a dynamic text
Text Tool

11. How to insert dynamic
text
Enter Line 1: in the
appearing dialog and
selecting line_1 from
the list of objects on
tab Objects of
the Advanced section
Select Line_1 represented by f
Tab Objects
Enter Static Part: Line1
Press Ok

12. How to insert dynamic
text
Create a dynamic text
with the static part
Line 2: and select
line_2 from the list
of objects on
tab Objects of the
Advanced section.
Select Line_2 represented by g
Tab Objects
Enter Static Part: Line2
Press Ok

13. How to insert dynamic
text
Construct the
intersection point A of
both line1 and line2 by
either using the
Intersect tool, or by
entering the
command
Intersect(line_1,
line_2)into the Input
Bar.

14. How to insert dynamic
text
Enter xcoordinate =
x(A) into the Input Bar.
Hint: x(A) gives you
the x-coordinate of
the intersection point
A
x coordinate

15. How to insert dynamic
text
Also, define
ycoordinate = y(A).
Hint: y(A) gives you
the y-coordinate of
the intersection point
A
y coordinate

16. How to insert dynamic
text
Create a dynamic text
with the static part
Solution: x = and
select xcoordinate
from the list of objects
on tab Objects and
Press Enter
x coordinate

17. How to insert dynamic
text
Create a dynamic text
with the static part
Solution: y = and
select ycoordinate
from the list of objects
on tab Objects and
Press Enter
ycoordinate

18. How to insert dynamic
text
Fix the texts so they
can’t be moved
accidentally by
selecting the texts and
opening the Style Bar.
Fix Object

19. How to show the trace of an object
• Objects can leave a trace in the Graphics View when
they are moved. There are two ways of showing the
trace of an object: Select the object whose trace you
would like to show. Use the Style Bar button to open
the Settings. Check Show Trace on tab Basic. OR
• Right-click (MacOS: Ctrl-click, tablet: long tap) an
object and check Show Trace in the appearing context
menu.

20. How to show the trace of an object
Then, modify the
construction so that
the object, whose
trace you turned on,
changes its position
and leaves a trace in
the Graphics View.
Trace

21. How to show the
trace of an object
Graph the derivative
of a function
by tracing the slope of
point A.
1
2
)
(
2


x
x
f

22. How to show the trace of
an object
Create a new point A
on function f.
Hint: Point A can only
be moved along the
function.

23. How to show the
trace of an object
Create tangent g to
function f through
point A.

24. How to show the
trace of an object
Create the slope of
tangent g using m =
Slope(g).

25. How to show the
trace of an object
Define point
S = (x(A), m).
Hint: x(A) gives you
the x-coordinate of
point A

26. How to show the
trace of an object
Connect points A and
S using a segment.

27. How to show the
trace of an object
Turn on the trace of
point S and move
point A.
Hint: Right-click point
S (MacOS: Ctrl-click,
tablet: long tap) and
select Show Trace.
Turn on the Trace here

28. How to show the
trace of an object
Move point A.

29. How to show the
trace of an object
Close the Algebra
View by unchecking
the corresponding
option in the View
Menu.
Uncheck Algebra View here

30. Do It Yourself
Change the equation of the initial polynomial f(x) to produce a
new problem. For example, enter f(x)= 2 x² into the Input Bar.
You might want to zoom if point A lays outside of the visible
area after changing the function.
Display the Input Bar using the View Menu

31. Learn more about the
Trace feature
The Show Trace
feature has some
special characteristics:
A trace is a temporary
phenomenon.
Whenever the
graphics are
refreshed, the trace
disappears (e.g. on
zoom). When you zoom, trace feature disappear

32. Learn more about the
Trace feature
If you want to display
a permanent trace of
a point you can use
the Locus tool or
command.
Locus tool

33. Learn more about the
Trace feature
The trace cannot be
saved and is not
shown in the Algebra
View.
You can turn off the
trace of an object by
unchecking Show
Trace either in
the Settings or the
context menu. Uncheck Show trace here

34. Learn more about the
Trace feature
The menu item Refresh
Views in the View
menu clears all traces.
Hint: If you are using
GeoGebra Desktop or
the Online or Tablet
App, you can also use
the key combination Ctrl
– F to refresh the Views.
Refresh Views

35. END
NEXT TOPIC:
continue…