1


2

 Viewing Window Size
 Graphing Equations
 Table Values
 X and YIntercepts

3

 Viewing Window Size (Screen size)
 This key brings up the screen that controls the size of the viewing
window.

4

 Xmin is the leftmost value on the xaxis
 Xmax is the rightmost value on the xaxis
 Xscl is the number of units between tick marks on the xaxis
 Ymin is the lowest value on the yaxis
 Ymax is the uppermost value on the yaxis
 Yscl is the number of units between tick marks on the yaxis
 Xres indicates how many pixels on the xaxis are skipped before another xvalue is
used to calculate y
 Viewing Window Size

5

 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.

6

 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.

7

 2:Zoom In  magnifies the
graph. You can change the center
of the zoomed window by moving the cursor before pressing ENTER
 The ZOOM MENU
 1:ZBox  allows you to draw a box around the part of the screen you want
to see in the window.

8

 4:Zdecimalsets the window so that each pixel along the xaxis
represents one tenth
 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

9

 6:Zstandardsets the window to the default window
 (xs go from 10 to 10;
 Ys go from 10 to 10)
 5:Zsquaresets the window so that the distance between tick marks on the
xaxis is the same as the distance between tick marks on the yaxis

10

 The ZOOM MENU  (Preset window sizes)
 7:ZTrigsets the window to show two revolutions and the tick marks to
represent multiples of 90
 8:Zintegersets the window so that each pixel along the xaxis
represents one
 9:ZoomStatfits the window to statistical data

11

 6:ZStandard
 0:ZoomFit
 The ZOOM MENU
 0:ZoomFitchanges 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

12

 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

13

 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

14

 Graphing Equations
 Graph the equation y = 3x 4
 Because we have y= form, this equation is ready to enter:
 Press

15

 Graphing Equations
 The window will show:
 Then press
 And the screen will show:

16

 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 =

17

 Graphing Equations
 Now you are ready to enter y =
 Press and enter
the expression
 Make sure you use parentheses in the numerator.

18

 Graphing Equations
 The window will show:
 Press
 And the screen will show:

19

 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.

20

 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.

21

 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

22

 The key
 Once you have the graph on the window, press to put the cursor on the
line.
 This will give you an xvalue
and a yvalue.
 For additional values, use the left and right arrow keys to move the
cursor forward and back.

23

 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.

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 Graph the line y = 3x 4 and label at least two points on the line.
 In ZOOM 6:Standard
 the window will show:

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 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).

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 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.)

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 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 y_{1.}
 You can create a table for all values of x or for
 particular values of x.

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 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),

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 The Table of Values
 So,how do you get to the
 TABLE of VALUES??

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 The Table of Values
 Enter the equation as Y_{1}:
 Press to graph
 Check your table settings

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 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.

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 TblStart tells where to start your values in the table
 Tbl  tells how much to increase your
xvalues by each time
 Independent AUTO will automatically compute your table without
asking for specific xvalues
 Dependent AUTO will
automatically compute the yvalues for the given xvalues
 The Table of Values

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 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.

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 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

35

 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

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 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),

37

 X and YIntercepts
 Defn: The Xintercept is the
point where the line crosses the xaxis.
 Defn: The Yintercept is the
point where the line crosses the yaxis.

38

 X and YIntercepts
 The X and YIntercepts are two points commonly used when labeling a
graph.
 We can use the calculator to find these two points.

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 How to find the YIntercept
 Because the yintercept is located on the yaxis, and because all points
on the yaxis have an x coordinate of 0, we are going to calculate the value
of y when x is 0.
 Enter the equation as y= and
graph
 Press

40

 Find the yintercept of the equation
 y = 3x 4

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 Enter the equation as y= and
graph
 Press
 To calculate 1:VALUE
 Press

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 To choose the xvalue of 0
 Press
 This gives a yvalue of 4, so the yintercept is the ordered pair
(0,4).

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 How to find the XIntercept
 Because the xintercept is located on the xaxis, and because all points
on the xaxis have a y coordinate of 0, we are going to find where the
y= equation is zero.
 Enter the given equation as y_{1}=
 Enter y_{2} = 0
(Recall that y = 0 is the xaxis.)
 Graph
 Find where the equation (y_{1}) intersects the xaxis (y_{2})

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 Find the xintercept of the equation
 y = 3x 4

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 Enter the equation as y_{1}=
 Enter y_{2} = 0
 Graph
 Calculate 5:intersect

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 Then it gives you the xvalue of 1.333333, which means the xintercept
is the ordered pair (1.33333,0).

47

 DISCLAIMER:
 All of the equations we will graph in Elementary Algebra will be lines
that have at most 1 xintercept and at most 1 yintercept. There are additional steps to be taken
if there is more than one xintercept.

48

 Find the xintercept and the
 yintercept of the equation

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 Find the xintercept and the
 yintercept of the equation
 Steps:
 Enter as y=
 Graph
 Find the xintercept
 Find the yintercept

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 Find the xint. and the yint. of the equation
 Enter as y_{1}=
 Enter y_{2} = 0
 Graph

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 Find the xint. and the yint. of the equation
 Your screens will look like this:

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 Find the xintercept
 (CALC 5:INTERSECT)

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 Find the xintercept
 The xintercept is the ordered pair (6,0)

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 Find the yintercept
 (CALC 1:VALUE)
 Enter the x value as 0

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 Find the yintercept
 The yintercept is the ordered pair (0,4)
