Graphing
Module 5
Graphing
Viewing Window Size
 Graphing Equations
 Table Values
 X- and Y-Intercepts

Graphing
Viewing Window Size (Screen size)
This key brings up the screen that
controls the size of the viewing
window.
Graphing
Viewing Window Size 






Xmin is the leftmost value on
the x-axis
Xmax is the rightmost value
on the x-axis
Xscl is the number of units
between tick marks on the xaxis
Ymin is the lowest value on
the y-axis
Ymax is the uppermost value
on the y-axis
Yscl is the number of units
between tick marks on the yaxis
Xres indicates how many
pixels on the x-axis are
skipped before another xvalue is used to calculate y
Graphing
Viewing Window Size
To change the window size, you can go down
and manually enter the specific values to be
changed or go to a preset screen size. To
manually enter new values, move the cursor
to where you want a new value and enter the
new value.
Graphing
To use the preset window values, you can
change the viewing window by using the
ZOOM menu.
Pressing the
gives us other
common window sizes.
Graphing
The ZOOM MENU-
(Preset window sizes)
1:ZBox - allows you to
draw a box around the
part of the screen you
want to see in the
window.
2:Zoom In - magnifies the
graph. You can change
the center of the
zoomed window by
moving the cursor
before pressing ENTER
Graphing
The ZOOM MENU-
3:Zoom Out – shrinks the
graph. You can change
the center of the graph
by moving the cursor
before you press
ENTER
(Preset window sizes)
4:Zdecimal-sets the
window so that each
pixel along the x-axis
represents one tenth
Graphing
5:Zsquare-sets the window
so that the distance
between tick marks on
the x-axis is the same
as the distance between
tick marks on the y-axis
6:Zstandard-sets the
window to the default
window
(x’s go from –10 to 10;
Y’s go from –10 to 10)
Graphing
The ZOOM MENU - (Preset window sizes)

7:ZTrig-sets the window to show two
revolutions and the tick marks to represent
multiples of 90

8:Zinteger-sets the window so that each pixel
along the x-axis represents one

9:ZoomStat-fits the window to statistical data
Graphing
The ZOOM MENU

0:ZoomFit-changes the
window so that both the
lowest and the highest
values of y are shown in
the window. This is
often an extreme case
of zooming in and out
and you may lose
details
6:ZStandard
0:ZoomFit
Graphing
The ZOOM MENU - (Preset window sizes)
For most of the things we will do this semester,
the Zoom 6:standard option will be the best
window viewing size. You can choose this
option by pressing
Graphing
Graphing Equations
In order to graph an equation (they will usually
have an x and a y variable), the equation must
be solved for y=
That is, y must be on a side by itself in order to
enter it into the calculator.
Yes:
y = 3x – 4
No:
2x + 3y = 6
Graphing
Graphing Equations
Graph the equation y = 3x – 4
Because we have y= form, this equation is
ready to enter:

Press
Graphing
Graphing Equations
The window will show:

Then press
And the screen will show:
Graphing
Graphing Equations
Graph 2x + 3y = 6
This equation is not ready to enter – why not???
You must first solve for y= form
and you will get y =  2 x  6
3
Graphing
Graphing Equations
 2x  6
Now you are ready to enter y =
3

Press
and enter the expression
Make sure you use parentheses in the numerator.
Graphing
Graphing Equations
The window will show:

Press
And the screen will show:
Graphing
Graphing Equations
The purpose for graphing an equation is to
show graphically all solutions that the
equation has. The graph consists of many,
many ordered pairs of the form (x,y). Each
of these ordered pairs is a solution to the
equation.
Graphing
Graphing Equations
Often we find several ordered pairs that are
solutions to an equation and use the points
to determine what the graph looks like.
Other times we will have the graph and
need to identify specific points on the
graph.
Graphing
Graphing Equations
Once you have the graph on the calculator
window, specific points on the line can be
found in a couple of different ways:
1. Using the
key
2. Using a table of values
Graphing
The
key
Once you have the graph on the window,
press
to put the cursor on the line.
This will give you an x-value and a y-value.
For additional values, use the left and right
arrow keys to move the cursor forward and
back.
Graphing
The
key
In Zoom 6:standard mode, additional values will
probably contain many decimal places,
however, if you trace in Zoom 8:integer mode,
“nicer” values will appear.
Example
Graph the line y = 3x – 4 and label at
least two points on the line.
In ZOOM 6:Standard
the window will show:
Example
To find some specific points, press
The window will show:
This gives you one ordered pair that is a
solution; that is, X = 0, Y = -4 denoted (0,-4).
Example
Use the left and right arrow keys to move the cursor
around to different points on the line.
This will give you additional points, but they will
probably be UGLY.
(Remember, try the ZOOM 8:INTEGER mode to
get nicer looking numbers.)
Graphing
The Table of Values
The second way to get specific points on the
graph is to use the table of values.
In order to do this, you need to have the
equation entered as y1.
You can create a table for all values of x or for
particular values of x.
Graphing
The Table of Values
The table of values will give you solutions to the
equation in a table format.
All of these ordered pair solutions will be points on the
line. So additional solutions are (-3, -13), (-1,-7), (2,2),…
Graphing
The Table of Values
So,how do you get to the
TABLE of VALUES??
Graphing
The Table of Values

Enter the equation as Y1:

Press

Check your table settings
to graph
Graphing
The Table of Values

Check your table settings
You will only need to do this the first time you want to
automatically create a table, then you will be able to
skip this step.
**See next screen for clarification.
Graphing
The Table of Values




TblStart – tells where
to start your values in
the table
 Tbl - tells how
much to increase your
x-values by each time
Independent – AUTO
– will automatically
compute your table
without asking for
specific x-values
Dependent – AUTO –
will automatically
compute the y-values
for the given x-values
Graphing
The Table of Values
NOTE: For typical table purposes, you will want
 Tbl to be 1 and both Independent and
Dependent to be on AUTO. TblStart can be
anything and can be adjusted later using the
up and down arrows.
Graphing
The Table of Values
Once the table is set up to your liking,

Press

Your window will show

You can get additional values by using the up and
down arrow keys
Graphing
Additional solutions
Example: For the equation y = 2x + 6, list five
ordered pairs that are solutions.
Use either the trace key or the table of values…
Graphing
Additional solutions
Example: For the equation y = 2x + 6, list five
ordered pairs that are solutions.
Enter the equation as y=
View the table:
Solns: (-3,0), (-2,2), …
Graphing
X- and Y-Intercepts
Defn: The X-intercept is the point where the line
crosses the x-axis.
Defn: The Y-intercept is the point where the line
crosses the y-axis.
Graphing
X- and Y-Intercepts
The X- and Y-Intercepts are two points
commonly used when labeling a graph.
We can use the calculator to find these two
points.
Graphing
How to find the Y-Intercept
Because the y-intercept is located on the y-axis,
and because all points on the y-axis have an x
coordinate of 0, we are going to calculate the
value of y when x is 0.


Enter the equation as y=
Press
and graph
Graphing
Find the y-intercept of the equation
y = 3x – 4
Graphing

Enter the equation as y=
and graph

Press
To calculate 1:VALUE
 Press
Graphing
To choose the x-value of 0

Press
This gives a y-value of -4,
so the y-intercept is the
ordered pair (0,-4).
Graphing
How to find the X-Intercept
Because the x-intercept is located on the x-axis,
and because all points on the x-axis have a y
coordinate of 0, we are going to find where
the y= equation is zero.




Enter the given equation as y1=
Enter y2 = 0
(Recall that y = 0 is the x-axis.)
Graph
Find where the equation (y1) intersects the x-axis (y2)
Graphing
Find the x-intercept of the equation
y = 3x – 4
Graphing

Enter the equation as
y1=

Enter y2 = 0

Graph

Calculate 5:intersect
Graphing
Then it gives you the x-value of 1.333333, which
means the x-intercept is the ordered pair (1.33333,0).
Graphing
DISCLAIMER:
All of the equations we will graph in
Elementary Algebra will be lines that
have at most 1 x-intercept and at most 1
y-intercept. There are additional steps to
be taken if there is more than one xintercept.
Example
Find the x-intercept and the
2
y-intercept of the equation y  x  4
3
Example
Find the x-intercept and the
y-intercept of the equation y  2 x  4
3
Steps:

Enter as y=

Graph

Find the x-intercept

Find the y-intercept
Example
Find the x-int. and the y-int. of the
equation y  2 x  4
3

Enter as y1=

Enter y2 = 0
Graph

Example
Find the x-int. and the y-int. of the
equation y  2 x  4
3
Your screens will look like this:
Example
Find the x-intercept
(CALC 5:INTERSECT)
Example
Find the x-intercept
The x-intercept is the ordered pair (6,0)
Example
Find the y-intercept
(CALC 1:VALUE)

Enter the x value as 0
Example
Find the y-intercept
The y-intercept is the ordered pair (0,-4)