A Tutorial for the TI-83 Plus Graphing Calculator
Introduction
The TI-83 Plus graphing calculator serves as a powerful tool for exploring models in
computational science that allow you to analyze real world science problems with
mathematics. This introduction to the calculator will show you some of the features you
will use in the project; but the calculator has many other capabilities.
As you read through this introduction, please have your calculator nearby and use it as
instructed to become familiar with its operation. Also, please keep handy the TI-83 Plus
Graphing Calculator Manual (the Manual), since you will be using it, too.
The graphic at right shows the calculator. When
you first turn on the calculator, it always displays
the home screen. (The home screen may have
numerical expressions or graphs from previous
sessions which may be deleted by pressing the
CLEAR key.)
You may recognize familiar keys as on other
calculators you have used, such as the white
number keys and blue arithmetic operators. There
is no EQUALS [=] key; the ENTER key is used
instead. Note the cursor keys in blue. These move
the cursor around the screen in the direction of
the white arrows on the keys. The black keys set
up functions or other special actions. The row of
narrow keys immediately under the screen are
used to define functions and to create tables and
graphs.
Notice the gold colored 2nd key and green
colored ALPHA key. These work as types of
shift keys to enable most other keys to serve two
or three other ways.
If the calculator’s batteries are not installed,
please do so now as the Manual indicates on
pages B-2 to B-3. (You will not need to change the
lithium battery.)
Page 9
Introducing the TI-83 Plus Graphing Calculator
Basic Calculator Operations
Read the Manual pages 1-2 and 1-3 for turning the calculator on and off. You will also
practice lightening and darkening the display. These operations further will give you a
sense of the way the 2nd key works.
Clear the home
screen.
Enter a number,
perform an
operation, or display
a function or menu
printed on the key.
Press the CLEAR key.
Perform the function
printed in gold
above the key.
Use the gold 2nd key to access the appropriate key
underneath the function written in gold. (Anytime you see
letters or a term enclosed in brackets [ ] in this introduction it
means to push the key right below the letters or term.) When
you press the 2nd key, the cursor will change to an arrow
pointing up while it waits for you to press the next key. This
arrow means that the next key you push will activate the
symbol or operation printed in gold above the key.
Press the key. (Pictures of the calculator keys will be shown in a
box
in this introduction.)
Example:
Press 3 + 5 ENTER to add 3+5.
Press MATH to see the MATH menu options.
Example:
Press 2nd [  ] to display the symbol for pi. Notice that when
you press ENTER the decimal value for pi appears.
Enter a letter or
character.
Use the green ALPHA key to access the character or letter
printed above it in green. To enter several letters in a row, press
2nd [A-LOCK]. The cursor changes to a blinking A. To stop
entering letters, press ALPHA .
Example:
Press ALPHA [A] to display the letter A on the screen. If there
is a value stored for the variable A, it will appear when you
press ENTER .
Return to the home
screen from any
other screen.
Press and release the 2nd key, then press [QUIT].
Page 10
Introducing the TI-83 Plus Graphing Calculator
Change the way a
number or graph is
displayed.
Use the MODE key and move the cursor to the type of display
you want, then press ENTER . The modes are described in
detail on pages 1-9 to 1-12 in the Manual.
Example:
Numbers are usually displayed with a floating number of
decimal places, or as many as is needed. To display numbers
with a fixed number of 2 decimal places, press MODE . Use
the cursor keys to move the blinking cursor to the 2 on the
second line and press ENTER . Press 2nd [QUIT] to return to
the home screen. Enter the number 5.236 and press ENTER .
The number should display as 5.24 rounded to 2 decimal
places. (Remember to press MODE again to set the display
back to Float.
Respond to an error
message.
If you try to enter an "illegal" operation, the calculator will
display an error message. You have 2 choices of how to
respond. You may press option 1:Goto to go back to the entry.
The cursor will be flashing at or after the place where the error
was made. The error can then be fixed. Your other choice is to
press option 2:Quit to return to the home screen. For a complete
listing of error messages, see pages B-6 to B-10 in the Manual.
Example:
To see what happens when you try to divide by zero, press 1
 0 ENTER . The screen display should look like this:
ERR:DIVIDE BY 0
1:QUIT
2:Goto
Press 1 or ENTER to quit and return to the home screen.
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Introducing the TI-83 Plus Graphing Calculator
Use the answer in
another calculation.
The answer to the last expression evaluated is stored as a
variable called Ans. To perform an operation on the last
answer, you can simply press the operation and other key(s)
required and the answer will be used as the first number in the
expression. To use the last answer in a new expression, press
2nd [ANS] at the location where the answer is needed.
Examples:
1) Add 20+3: Press 2 0 + 3 ENTER
return 23.
2) Multiply this last answer by 5.
Press 2nd [ANS]  5 ENTER.
The display should show:
Ans*5
115
. The display will
3) If you begin an entry with an arithmetic operation, the
calculator will assume you mean to operate on the value in
[ANS], and will supply it automatically. Suppose you now want
to divide the last answer by 2.
Press  2 ENTER and the answer is 57.5 since the value
stored in [ANS] was 115.
The display will show:
Ans/2
57.5
4) Calculate the sum of 13.6 and 20.2, then divide 150 by the
result.
Press 1 3 . 6 + 2 0 . 2 ENTER
Press 1
5 0  2nd [ANS] ENTER
The display should show:
13.6 + 20.2
33.8
150/Ans
4.437869822
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Introducing the TI-83 Plus Graphing Calculator
Repeat an entry to
perform another
calculation.
Press 2nd [ENTRY] to repeat the last entry on the screen. It may
then be edited and executed again. If you continue to press 2nd
[ENTRY], you will be able to access earlier entries that you can
edit or execute. The Last Entry storage area keeps as many
previous entries as possible until it is full.
Edit an entry.
Press one of the cursor keys to move around the screen. You
may simply reenter a number or symbol over the blinking
cursor.
To insert new numbers or symbols, press 2nd [INS]. The cursor
changes from a solid blinking square to a blinking underline
showing that you are in insert mode. Once you move the cursor
or press ENTER , then you will return to normal mode.
To delete numbers or symbols, press the DEL key. It will delete
the character at the cursor.
Manage the memory
in the calculator.
Press 2nd [MEM] to access the MEMORY menu. Option 1: About
will display the operating system version in the calculator. If
you need to free up some memory to run new items such as
programs, you may need to delete some items. Option 2: Mem
Mgmt/Del... will give a list of choices from which items may be
deleted. Do not delete from memory unless you know exactly
what you are doing; items deleted from memory cannot be
retrieved. See pages 18-1 to 18-20 in the Manual for more
information about memory management.
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Introducing the TI-83 Plus Graphing Calculator
Numerical Computations
Add, subtract,
multiply or divide
integers or decimals.
Enter the numbers and operation symbols required. Press
ENTER to see the result. The logic of the calculator uses the
standard for order of operations, which means basic operations
are performed in this order: 1) operations in parentheses; 2) all
multiplication and division from left to right; 3) all addition and
subtraction from left to right. To enter a negative number, first
press the ( - ) key on the bottom row. Do not press the blue
subtraction key. See page 1-23 in the Manual for more
information on the order of evaluation in an expression.
Example:
Calculate 13.6 + -8(6.3  5)
Press 1 3 . 6 + ( - ) 8
The display should show:
13.6 + -8(6.3  5)
3.2
Operate with
fractions.
( 6
.
3
 5
) ENTER
An answer to a rational expression can be expressed either as a
decimal or a fraction. The result of fraction operations will be
expressed as a decimal unless you choose to express it as a
fraction. Option 1:Frac on the MATH menu will express the
result as a fraction. To express a fraction as a decimal, choose
option 2:Dec from the MATH menu.
Examples:
1 1
 Add 2 + 3.
Press 1  2 +
MATH
1  3
1 ENTER
The display should show:
1/2 + 1/3 Frac
5/6
 Display 0.525 as a fraction.
Press 0
5 MATH
. 5 2
The display should show:
0.525 Frac
21/40
Page 14
1
ENTER
Introducing the TI-83 Plus Graphing Calculator
Use exponents, roots, Raising a number to a power or finding a root can be done in
and radicals.
several ways. The most common operations of squaring a
number or finding the square root can be found directly on the
keyboard. Cubing a number or finding the cube root are
options which are found on the MATH MATH menu. To raise to
other powers or roots, press the ^ key after the expression
that you are raising to a power, then enter the power. (If you
use option 5 on the math menu, x , you must enter the value
for x first, then select option 5, press ENTER , then enter the
number for which you wish to find the root.)
Examples:
ENTER .
X2
To find 252, press 2 5
To find 25 , press 2nd [
] 2 5 ENTER .
3 ENTER .
To find 53, press 5 MATH
4 6 4 ENTER .
To find 3 64 , press MATH
4
To find 5 , press 5 ^ 4 ENTER .
To find 4 81 , or 81.25, press 8 1 ^ . 2 5 ENTER
1  ) ).
(or 8 1 ^ (
Find absolute value.
Finding the absolute value is found on the MATH NUM menu.
Press MATH , then use the blue right cursor key to move to the
NUM menu at the top of the screen. The first function listed
there, 1:abs( , finds the absolute value.
Example:
To find | -8 |, press MATH
To find | -8 + 3 |, press MATH
ENTER .
Page 15
1 (-)
8
1 (-)
ENTER .
8 + 3 )
)
Introducing the TI-83 Plus Graphing Calculator
Use scientific
notation.
To enter a number written in scientific notation, use the [EE] key
to express the power of 10.
Example:
Enter 9.5 x 10-3 on the calculator.
Press 9 . 5 2nd [EE] ( - )
3 .
The display should show:
9.5E-3
.0095
To display numbers and results in scientific notation, the
MODE settings must be changed to Sci. To do this, press
MODE
ENTER . Make sure that Sci has been
highlighted. Press 2nd [QUIT] to return to the home screen.
Enter the number 189654.2 and press ENTER . The display
should show:
189654.2
1.896542E5
To return the display to normal, press MODE , choose
Normal, and press ENTER .
Store numbers to
variables to use in
calculations.
You can store values to letter names (ALPHA characters) to use in
future expressions or calculations. All the letters of the alphabet
plus the Greek letter theta (  ) are available to store real
number values. Be aware that the letter X is the variable used to
define functions for graphing, so you may choose to use other
letters when you are not defining a function.
To store a value in a variable, press the value you want to store,
followed by STO> ALPHA followed by the key with the
green letter above it.
To display the value that has been stored in the variable, press
2nd [RCL] ALPHA followed by the key with the green letter
above it. The key [RCL] stands for "recall."
Page 16
Introducing the TI-83 Plus Graphing Calculator
Store numbers to
variables to use in
calculations (con’t.).
Example:
Find the Celsius temperatures for 32°F, 72°F, and 98°F.
The formula for changing degrees Fahrenheit to degrees Celsius
5
is C = 9(F  32). When you enter the formula and press ENTER
the result you see will be evaluated for whatever value was
stored for the letter F. You can store a value as F, execute the
formula, store another value as F, press 2nd [ENTRY] twice to
retrieve the formula, and evaluate it for the new value of F, and
so on until you have calculated the Celsius values for all the
values of F.
Press 3 2 STO> ALPHA [F] ENTER
ALPHA [F] Press ( 5  9 ) (
ENTER
Press 7 2 STO> ALPHA [F] ENTER
3
2
)
Press 2nd [ENTRY] 2nd [ENTRY] ENTER
Press 9 8 STO> ALPHA [F] ENTER
Press 2nd [ENTRY] 2nd [ENTRY] ENTER
The display should show:
32F
32
(5/9)(F  32)
0
72F
72
(5/9)(F  32)
22.22222222
98F
98
(5/9)(F  32)
36.66666667
The screen will only display 8 lines at a time, so the above
results will scroll down line by line. Make sure you record each
result before you enter the next one.
Page 17
Introducing the TI-83 Plus Graphing Calculator
Functions and Graphing
Functions are defined by using the  key. Once a function has been defined, you can
evaluate it directly, create a table of values, or graph it.
Enter a function.
Use the Y= to see a list of functions labeled Y1, Y2, Y3, etc.
You can enter up to 10 functions at a time. To enter a function,
place the cursor directly to the right of the = sign and enter the
function, using X as the variable. Recall that the variable X is
easily entered by pressing the X,T,,n key. Press ENTER
when you have completed the entry. You will notice that the =
sign has been highlighted. This means this is the "active"
function. To "turn off" the function Y1, put the cursor on the =
sign and press ENTER . Press ENTER again to turn it back
on. Press 2nd [QUIT] to return to the Home screen.
Example: Enter 2x + 5 as the first function.
Press Y= , then press 2 X,T,,n + 5
2nd [QUIT] to return to the Home screen.
Evaluate a function.
ENTER . Press
To find the value of a function at a particular value of X, use the
 key, move the cursor right to choose [Y-VARS] menu, press
ENTER , and choose 1:Function on the resulting menu.
Choose the function you wish to evaluate and press ENTER .
The function name will appear on the screen. Press ENTER
once more. The value of the function for the stored value of X
will appear.
Example: Evaluate Y1 for the values X = 2 and X = -1.
Press  to be sure that Y1 is defined as 2x + 5. Press 2nd [QUIT]
to return to the Home screen.
Press 2 STO> X,T,,n ENTER VARS
ENTER
ENTER ENTER . The value 9 should appear on the right of
the screen.
To evaluate for X = -1, press ( - )
1 STO> X,T,,n
ENTER VARS
ENTER ENTER ENTER . The
value 3 should appear.
Page 18
Introducing the TI-83 Plus Graphing Calculator
Create a table of
To show a table of values for the function Y1, you can use the
values for a function. table feature. Before showing a table for a function, first set up
how you want to display the table. You may choose to have the
calculator generate a table of values automatically or you can
choose to enter individual specific values X. If you want the
table to be generated automatically, you will enter the
minimum value of X to evaluate and specify the difference
between the remaining X-values to be evaluated.
Examples:
1) Show a table of values for the function Y = 2x + 5 generated
automatically from a minimum value of X = -5, with an
increment of 1 in the X values.
To set up a table to be automatically generated, press 2nd
[TblSet]. Enter the first value of X to be evaluated as TblStart = -5.
Enter the difference, or increment, between X values as Tbl = 1.
Put the blinking cursor on Indpnt: Auto and press ENTER to
generate X, the independent variable, automatically. Put the
blinking cursor on Depend: Auto and press ENTER to
generate the Y values automatically. (If you choose Depend:
Ask, the calculator will generate X values automatically, but
leave the Y values blank. When you press ENTER at each
value of X, it will calculate the Y value.)
Press Y=
to be sure 2x + 5 is entered as Y1. Press 2nd [QUIT]
to return to the Home screen. Press  [TABLE]. The table should
display on the screen with both X and Y1 values shown,
beginning with -5.
2) Build a table of values for the function y = 2x + 5 by entering
individual values for X.
To set up a table to enter specific values of X, press 2nd
[TblSet]. The TblStart and Tbl values will be ignored. Put
the blinking cursor on Indpnt: Ask and press ENTER . (The
choices for Depend are the same as above.
If Depend:Auto is selected, the calculator will immediately
display the Y value for each X entered. If Depend:Ask is
selected, the Y value will not be calculated until you press
ENTER at each location of Y.)
Page 19
Introducing the TI-83 Plus Graphing Calculator
Create a table of
values for a function
(con’t.).
Press  to be sure 2x + 5 is entered as Y1. Press  [QUIT] to
return to the Home screen. Press 2nd [TABLE]. A blank table
will display. Enter a value for X, then press ENTER to see the
Y value displayed.
Graph a function.
To graph the function entered in Y1, use GRAPH . The
function will display on the grid using the parameters set up in
the Mode and Window settings.
Use MODE to be sure the setting is on Func on the fourth row
to graph functions. Choose CONNECTED if you want to plot a
graph in which each point is connected to the next by a line.
Choose DOT to plot only the points that are calculated. Usually
you will want to plot graphs that are connected, but sometimes
the dot mode is preferable. The other types of graphing are
explained on page 3-4 in the Manual.
Use  to see the values for the display of the viewing window.
Xmin, Xmax, Ymin and Ymax define the boundaries of the
coordinate plane that will show in the window. Xscl and Yscl set
the distance between the tick marks on the X- and Y-axes. The
standard viewing window settings are: Xmin = -10, Xmax = 10,
Xscl = 1, Ymin = -10, Ymax = 10, Yscl = 1. You can change these
settings directly to display any area of the graph you wish to
see. Pressing ZOOM 6 sets the standard viewing values
automatically.
Notice that the viewing window of the calculator is not square.
When you use the standard window settings, the intervals on
the X- and Y-axes will not be the same size. There are several
ways to get a more "user friendly" window where the intervals
on the X- and Y-axes are the same; one is by pressing ZOOM
5 .
Use 2nd ZOOM (this opens the FORMAT screen) to see or
change how a graph appears. The FORMAT screen allows you to
display a graph in rectangular or polar coordinates, display the
x- and y-coordinate values at the bottom of the screen, and turn
the grid points, axes, and labels on or off. Be sure the RectGC is
highlighted so you will be graphing on the rectangular
coordinate grid. It's a good idea to leave the coordinates and
axes on. The grid and labels can be on or off as you choose.
Page 20
Introducing the TI-83 Plus Graphing Calculator
Graph a function
(con’t.).
Examples:
1) View the graph of 2x + 5 using the standard window
settings.
Press Y= to be sure that Y1 = 2x + 5 is entered and "turned on"
(the = sign must be highlighted). Press WINDOW and enter
the following settings: Xmin = -10, Xmax = 10, Xscl = 1, Ymin = 10, Ymax = 10, Yscl = 1. Press GRAPH to see the graph
displayed.
2) View the graph of 2x + 5 using 4 non-standard window
settings.
Press WINDOW to enter the new settings from each column
below, then press GRAPH to see how the display of the graph
has changed.
a
b
c
d
-47
-5
-4.7
0
Xmin =
47
5
4.7
10
Xmax =
10
.5
1
1
Xscl =
-31
-5
-3.1
-5
Ymin =
31
5
3.1
5
Ymax =
10
.5
1
1
Yscl =
Notice how the view of the graph changes with each new set of
window settings. With a wider range between maximum and
minimum values of x and y, you can see more of the graph, but
it can be harder to read. A good rule of thumb is to make the
scale factor about 10% of the width of the viewing window.
What happened when you entered the settings in "d"? Why
didn't you see any of the graph in the viewing window?
(Because the graph crosses the y-axis at the point (0, 5) and no
part of it appears in the defined window.)
Now press WINDOW and return the window settings to the
standard settings: Xmin = -10, Xmax = 10, Xscl = 1, Ymin = 10, Ymax = 10, and Yscl = 1. Press GRAPH to display the
graph of y = 2x + 5.
Page 21
Introducing the TI-83 Plus Graphing Calculator
Explore a graph with
the cursor or with
TRACE.
When you first display a graph, there is no cursor shown on the
screen. As soon as you press one of the cursor keys,
,
,
, or
, the cursor will appear in the center of the screen.
The cursor moves from dot to dot on the screen. As it moves,
you can see the x- and y-coordinate values of the cursor
position displayed on the bottom of the screen. Notice that it is
difficult to tell with exact accuracy if the cursor is really "on" the
graph or not. To guarantee that you are naming a point on the
graph, you must use the TRACE function.
To use the TRACE function, press the TRACE key. The cursor
will be shown on the first selected function in the list at the
middle X value on the screen. Press
and
to move the
cursor along the function and watch the values change at the
bottom of the screen. If you keep tracing a function above or
below the viewing window, the cursor disappears, but the
coordinate values still display at the bottom of the screen. If you
trace off the left or right edge of the screen (past the Xmin or
Xmax values), the viewing window will adjust automatically to
the left or right. To adjust the viewing window up or down so
that the cursor is at the center, press ENTER . This is a
"QuickZoom" feature that changes the Xmax, Xmin, Ymin, and
Ymax values but leaves the Xscl and Yscl values the same.
If you have more than one function graphed on the screen,
press the
or
cursor key to move to a different function to
trace its values. To turn off the TRACE function but keep the
graph displayed, press CLEAR
. You can also leave the
TRACE function by pressing another key or 2nd [QUIT] to
return to the home screen.
Example:
Trace the graph of y = 2x + 5.
Press TRACE . The blinking cursor should appear on the point
(0,5) because the middle X value shown on the screen is X=0
and the value of the function at that point is 5. Experiment with
the TRACE feature by pressing the right and left cursor keys and
watch the blinking cursor move along the graph. Notice how
the values of X and Y shown at the bottom of the screen change.
Press CLEAR to turn off the TRACE function.
Page 22
Introducing the TI-83 Plus Graphing Calculator
Explore a graph
using ZOOM.
You can use the ZOOM features to change quickly the viewing
window around a graph without recalculating the WINDOW
settings. The ZOOM features are explained fully on pages 3-20 to
3-24 in the Manual. Several of these are very useful and you
should be familiar with them. To use one of the ZOOM features,
press the ZOOM key and select the desired feature, then press
ENTER or just push the number that corresponds to the
desired feature.
Explore the graph of y = 2x + 5 by using the following features
from the ZOOM menu.
6:ZStandard resets the window variables to the standard
settings and replots the graph immediately.
5:ZSquare adjusts the window variables in one direction only so
that the distances between tick marks on the x- and y-axes are
the same. This makes the graphs "look right." For example, a
circle will look like a circle should look. The Xscl and Yscl
variables remain unchanged. The graph will be replotted
automatically with the new settings. This feature is one you will
use often.
8:ZInteger adjusts the window settings so that the x- and y-axes
values are integers. After you choose ZInteger, you may move
the cursor to the point you want for the center of the viewing
window. You must press ENTER to replot the graph using the
new settings. This feature is useful if you want to check integer
values for the x-coordinates of the function.
2:Zoom In magnifies the graph around the cursor location. After
you choose Zoom In, you may move the cursor (which now
looks like a +) to the location that you want to be the center of
the new window. Then press ENTER to zoom in. You can
keep zooming in by pressing ENTER again and again.
3:Zoom Out displays a greater portion of the graph around the
cursor location. It works just like Zoom In.
Page 23
Introducing the TI-83 Plus Graphing Calculator
Explore a graph
using ZOOM. (con't.)
1:ZBox allows you to draw a box on the screen to set the area
that you want to zoom in on in the viewing window. After you
select ZBox from the ZOOM menu, you will see the zoom cursor
that looks like a + sign. Move this cursor to any position that
you want to be a corner of the box you want to draw. Press
ENTER to establish a corner of the box. Now draw the box by
moving the cursor keys away from the corner you selected.
When you have the box you desire, with the cursor in the
opposite corner from the original corner, press ENTER again.
The graph will be replotted in the new viewing window.
To cancel a ZOOM function before it takes effect (before you
press ENTER ), just press CLEAR . To leave the ZOOM
function, press any other function key or 2nd [QUIT] to return
to the home screen.
You have now learned and practiced many of the basic features of the TI-83 Plus
calculator. Complete the exercises in the Introductory Practice Set and Comparing
Graphs of Several Equations that follow. Check your answers with the Solution Key at
the end of this section.
Page 24
Introducing the TI-83 Plus Graphing Calculator
INTRODUCTORY PRACTICE SET
Use the TI-83 Plus to evaluate the following expressions and solve the following
problems.
1. 4.56 x 2.91
2. 896  23
3. 92
1
4.  
 2
3
5. 154
6. - 16
7.
2 1
- (Write the answer as a fraction.)
3 4
8. Change
5
to a decimal.
16
9. Change 0.875 to a fraction.
10. 4 19 + 3 27 (Write the answer as a fraction.)
11. 16  4(3 + 7)
12.
32 - 52
16 + 8
13. 289
14. 3 - 4096
15. 4 1296
16. 642.14
17. 3( - 8 + 11) - 17
Page 25
Introducing the TI-83 Plus Graphing Calculator
18. 8.635 x 105 x 7.18 x 10-7 . Express the result as a standard numeral and in scientific
notation.
19. Use the formula d = r  t to find the distance given the rate and time. Store the values
for r and t in R and T on the calculator, then find R  T.
a) Find d when r = 55 mph and t = 2 hours.
b) Find d when r = 55 mph and t = 3 hours.
c) Find d when r = 63 mph and t = 2.5 hours.
Page 26
Introducing the TI-83 Plus Graphing Calculator
Comparing Graphs of Several Equations
You can graph more than one equation at a time on the TI-83 Plus. This may be useful
to compare different equations.
Before beginning the following exercises, set the viewing window so that it is square.
First press ZOOM 6 to select ZStandard, then ZOOM 5 to choose ZSquare so
the distances on the horizontal and vertical axes are the same.
Part A
Graph the following equations, adding one at a time on the same screen. To do this,
press Y= . The cursor should be flashing in the first position after the = sign for Y1. If
there are any previous equations, press CLEAR to erase them. To enter y = x, press
, X,T,,n then press GRAPH to display the graph of Y1. To add the second equation,
press Y= . Press the
key to move to the second equation. Press X,T,,n + 1 ,
then GRAPH to display both Y1 and Y2 on the same screen. Repeat the process to
graph the remaining equations.
1.
2.
3.
4.
5.
y1 = x
y2 = x + 1
y3 = x + 2
y4 = x  3
y5 = x  5
Answer the following questions:
6. What is the same about these 5 lines?
7. What is different?
8. How does the number being added to or subtracted from X affect the graph of
the line?
Part B
Using the same procedure as in part A, graph the following equations. Be sure to clear
all equations from Part A first.
1.
2.
3.
4.
y1 = x
y2 = 3x
y3 = 6x
y4 = 13x
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Introducing the TI-83 Plus Graphing Calculator
1
5. y5 = 2x
Answer these questions:
6. What is the same about these 5 lines?
7. What is different?
8. How does multiplying the X by a constant affect the graph?
Part C
Clear all equations from Part B. Then graph the following equations, one pair at a time,
using the same process as in Part A: (First enter Y1 and Y2 and graph, then enter Y3 and
Y4, etc.)
1.
2.
3.
4.
y1 = x
y2 = -x
y3 = 3x
y4 = -3x
1
5. y5 = 2x
1
6. y6 = -2x
Answer these questions:
7. How does multiplying the X by a negative number affect the graph of a line?
8. The equation of a line can be written in the general form of y = mx + b, where m
is the slope and b is the y-intercept. What affect does changing the y-intercept
have on the graph of a line if the slope remains the same?
9. What is the difference between the graph of a line with a positive slope and the
graph of a line with a negative slope?
10. Which of the following lines have steeper slants? Explain.
a. y = 3x
or
y=x
b. y = 4x + 5
or
y = 4x + 5
c. y = 2x + 1
d. y = -x + 5
or
or
y = 2x  1
y = -5x + 5
e. y = -2x
or
y = -2x
f. y = 3x + 7
or
y = -3x  11
1
1
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Introducing the TI-83 Plus Graphing Calculator
Answer Key for Introductory Practice Set
The calculator display for each answer should be as follows:
1. 13.2696
2. 38.95652174
3. 81
4. .125
5. 50625
6. 16
5
7. 12
8. .3125
9. 78
10.
466
63
11. -24
12. .2916666667
13. 17
14. -16
15. 6
16. 1.699850313E11
17. 8
18. .619993 and 6.19993E-1
19. a) d = 110 b) d = 165 c) d = 157.5
Answer Key for Comparing Graphs of Several Equations
Part A:
6. The lines all have the same slope (or they all point up to the right at the same slant.
7. They cross the y-axis at different places.
8. It moves the line up or down the y-axis.
Part B:
6. They all have a positive slope and they all go through the point (0, 0).
7. They have different slopes; some are steeper than others.
8. The greater the value of the constant, the steeper the slope of the line.
Part C:
7. Multiplying x by a negative number gives the line a negative slope.
8. Changing the y-intercept only moves the line up or down the y-axis without
changing the slope.
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Introducing the TI-83 Plus Graphing Calculator
9. The graph of a line with positive slope points up to the right on the graph; the graph
of a line with a negative slope points down to the right.
10. a. y = 3x has a steeper slant because 3 > 1 (y = x is the same as y = 1x)
b. y = 4x + 5 is steeper because 4 > 14 .
c. Both lines have the same slant. They cross the y-axis at different places.
d. y = -5x + 5 is steeper than y = -x + 5.
e. y = -2x is steeper (negatively) than y =  21 .
f. The two lines have the same “steepness,” by one is positive and one is negative.
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