# ti-83 graphing linear equations activity

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```					 Graphing Linear Equations

Time Span: One week (5 classes)

Tools: TI 83 Graphing Calculators

TI Interactive

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Overall Objectives for the Unit:

Students will be able to:

1.) Label and identify axes, quadrants, and origin
2.) Plot points
3.) Graph linear equations
4.) Identify positive and negative slope
5.) Identify y-intercept
6.) Visually identify slope using Rise/Run
7.) Graph equations using y-intercept/slope method
8.) Rewrite equations into y = mx + b form
9.) Graph equations using y-intercept/slope method
10.) Be proficient in adjusting window/using zoom on TI Calculator
11.) Recognize the relationship between slope and parallel lines
12.) Recognize the relationship between slope and perpendicular lines.

New York State Standards:
1.) MST Standard 1: Analysis, Inquiry
2.) MST Standard 2: Technology
3.) MST Standard 3: Mathematics

NCTM Standards:
1.) Algebra Standard
2.) Geometry Standard
3.) Reasoning and Proof Standard
4.) Communication Standard
5.) Connections Standard
6.) Representation Standard

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Resources Used

1.) Textbook, McDougal Littell, Algebra 1, Chapter 4, pages 203-250, 2004.

2.) TI 83 Graphing Calculator

3.) TI Interactive – used to create worksheets

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Materials and Equipment Needed

Day 1:   Graph paper

Large White Board with Axes on it/Dry Erase Markers

TI 83 Graphing Calculators

Day 2:   Graph paper

TI 83 Graphing Calculators

Large White Board with Axes on it/Dry Erase Markers

Day 3:   Graph paper

TI 83 Graphing Calculators

Large White Board with Axes on it/Dry Erase Markers

Day 4:   Graph paper

TI 83 Graphing Calculators

TI Interactive Worksheet- Parallel Lines

Day 5:   TI 83 Graphing Calculators

TI Interactive Worksheet- Perpendicular Lines

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Overview of the entire 5-day unit

Day 1:   Review of Graphing Basics:
-labeling and identify axes, quadrants, and origin
-plotting ordered pairs, graphing linear equations, and slope.

Day 2:   Y-Intercept/Slope Method of Graphing Equations
- Identify y-intercept
- identify slope using Rise/Run
-graph equations using y-intercept/slope method
Day 3:   Rewriting equations into Y = mx + b form
- rewrite equations into y = mx + b form

- graph equations using y-intercept/slope method

- adjusting window/using zoom on TI Calculator
Day 4:   Discovering Parallel Lines
- identifying the relationship between slope and parallel lines
- writing equations of parallel lines
Day 5:   Discovering Perpendicular Lines
- identifying the relationship between slope and perpendicular lines
- writing equations of perpendicular lines

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Lesson Plan (Day 1)

Topic: Review of graphing basics

New York State Standards: MST Standard 1: Analysis, Inquiry

MST Standard 2: Technology

MST Standard 3: Mathematics

Materials:     Graph paper

Large White Board with Axes on it

TI 83 Graphing Calculators

Objectives:    Students will be able to:

1.) Label and identify axes, quadrants, and origin

2.) Plot points

3.) Graph linear equations

4.) Identify positive and negative slope

Opening Activity:     Have students come up to the board to label as many things as possible on

the graph. Students will label their own graphs. X-axis, Y-axis, origin, and quadrants should all

be labeled. Ask students what sign (positive or negative) a point would have in each quadrant.

Main Instruction:     After plotting several points, students will be asked to graph the following:

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A.) y = 2x + 4           B.) y = x + 2          C.) y = -2x -3

Students will be shown how to graph each equation by creating a table and finding three correct

solutions. If any students can graph using the y-intercept/slope method they will be encouraged

to do so individually, but they must demonstrate an ability to graph equations using a table as

well. After the three lines are graphed, a discussion will begin about slope. Examples A & B will

be used for positive slope and example C will be used for negative slope.

Students will then explore the following equations with the graphing calculator to gain a

better understanding of slope:

D.) y = 3x + 6            E.) y = -x + 7         F.) y = - 4x   G.) y = 2x

Closing Activity:       Students will be asked to explain slope to their partner. Students will have

to construct and graph two equations, one with positive slope and one with negative slope.

Homework: Textbook, page 206# 10-26(evens) and page 214# 21-23

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Lesson Plan (Day 2)

Topic: Y-Intercept/Slope Method of Graphing Equations

New York State Standards: MST Standard 1: Analysis, Inquiry

MST Standard 2: Technology

MST Standard 3: Mathematics

Materials:     Graph paper

TI 83 Graphing Calculators

Large White Board with Axes on it

Objectives:    Students will be able to:

1.) Identify y-intercept

2.) Visually identify slope using Rise/Run

3.) Graph equations using y-intercept/slope method

Opening Activity:      Students will be asked to graph the equation (y = 2x + 4) using a table and

finding three solutions.

Main Instruction:      Students will be asked if there is another way to graph this equation

besides using a graphing calculator. Hopefully, some students will have previously used the y-

intercept/slope method of graphing a line. If not, the method will be demonstrated by having

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students use the above example. Slope will be explained using Rise/Run for graphing purposes.

The y-intercept will be identified as the point where the equation crosses the y-axis. For the

opening activity the y-intercept is 4. Students will start at 4 on the y-axis, then use the

slope(rise/run) to plot a point up 2 and over 1.

Closing Activity:      Students will be asked to graph the following using this method:

A.) y = 3x + 5         B.) y = -x +2           C.) y = 4x –2           D.) y = -x

Students will be asked to check their partner's graphs by using the graphing calculator.

Homework:        Textbook, page 244#13-29 (odds)

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Lesson Plan (Day 3)

Topic: Rewriting equations into Y = mx + b form

New York State Standards: MST Standard 1: Analysis, Inquiry

MST Standard 2: Technology

MST Standard 3: Mathematics

Materials:     Graph paper

TI 83 Graphing Calculators

Large White Board with Axes on it

Objectives:    Students will be able to:

1.) Rewrite equations into y = mx + b form

2.) Graph equations using y-intercept/slope method

3.) Be proficient in adjusting window/using zoom on TI Calculator

Opening Activity: Students will be asked to graph the equation, y = 2x + 12, using the y-

intercept/slope method learned the previous day in class. Students will be asked to check their

graphs by using a graphing calculator. Questions should arise about not being able to view the y-

intercept on the calculator. Students will be shown how to adjust the window and use the zoom

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function to manipulate the screen. For the above equation, the students will change the YMAX in

the WINDOW to 20. This will allow them to see the y-intercept better.

Main Instruction:      Students will be asked to graph the equation, 2x + y = 7. Questions should

arise immediately because they have not graphed an equation that was not in y = mx + b form.

Students will be asked how we can manipulate the equation to the form we want. Since the

students have already practiced solving equations algebraically, this should not be a major

problem. The above equation will be re-written to: y = -2x + 7. Students will then graph the

equation.

Students and their partners will be asked to put the following equations in the proper

form and graph them:

A.) 2y = 4x + 10       B.) x = 5 + y         C.) 2x + 3y = 9        D.) 10- y = 2x

Closing Activity: Students will create 2 problems for their partner that are not in y= mx + b

form. Then, they will have to rewrite each other's problems and graph them. The graphing

calculator must be used to verify their graphs and the WINDOW changed if necessary on the

calculator.

Homework: None

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Lesson Plan (Day 4)

Topic: Discovering Parallel Lines

New York State Standards: MST Standard 1: Analysis, Inquiry

MST Standard 2: Technology

MST Standard 3: Mathematics

Materials:     Graph paper

TI 83 Graphing Calculators

TI Interactive Worksheet- Parallel Lines

Objectives:    Students will be able to:

1.) Recognize the relationship between slope and parallel lines

Opening Activity: Students will be asked to rewrite the following equations into y = mx + b

form and graph them on their graphing calculator:            A.) 4 = y –2x           B.) -2x + y = 1

Students will be asked if what conjectures they can make about the lines. Hopefully, the response

will be that they are parallel. They will be asked if anything in the two equations is the same.

Students should indicate that both equations have a slope of 2.

Main Instruction: Students will graph the following equations on their calculators:

C.) y = 4x + 2         D.) y = 2x + 6          E.) y = 4x             F.) y = 2x –2

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Students will be asked what they notice about equations? The connection between parallel lines

and slopes should start to develop. Students should identify that the equations with a slope of

four are parallel and the equations with a slope of 2 are parallel.

Closing Activity: Students will work independently on the following worksheet.

Homework: Finish worksheet.

1.) The lines are parallel.     2.) Slope of 3         3.) Slope of 3

4.) y = x + 4 (red)      y = x (blue)   y = x-4 (green)

5.) They are parallel.          6.) They all have the same slopes.

7.) Lines that are parallel have the same slope.

8.) Yes, they are parallel

9.) They all have the same slope.

10.) Yes, they will always be parallel.

11.) Answers will vary, but all equations should have the same slope.

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Parallel Lines                                     Name _____________________________

Mr. Swiech                                         Date _________

The following equations are graphed below:                y = 3x + 2 (blue)     y = 3x 4 (red)

1.) What do you notice about the lines? _________ 2.) What is the slope of the blue line? _____

3.) What is the slope of the red line? ________

4.) Graph the following equations:   y=x+4         y=x           y= x - 4

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5.) What do you notice about these lines? _________

6.) Do all the lines have the same slope? __________

7.) Can you make any connection between lines and their slopes?

____________________________________________________________

8.) Are these 3 linear equations parallel?__________        9.) Why? __________________

10.) Are linear equations that have the same slope always parallel?

______________________________________________________________________________

11.) Write 3 equations that are parallel.

___________________________

___________________________

___________________________

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Lesson Plan (Day 5)

Topic: Discovering Perpendicular Lines

New York State Standards: MST Standard 1: Analysis, Inquiry

MST Standard 2: Technology

MST Standard 3: Mathematics

Materials:     TI 83 Graphing Calculators

TI Interactive Worksheet- Perpendicular Lines

Objectives:    Students will be able to:

1.) Recognize the relationship between slope and perpendicular lines.

Opening Activity: Students will be asked to graph the following equations on their graphing

calculators:           A.) y = -2x + 6        B.) y = _ x – 4

Students will be asked if any relationship exists between the lines. Students will conjecture that

the lines are perpendicular, but most will not see any reason why yet. Students are asked to graph

another set of lines on their calculators:    C.) y = 5x             D.) y = -1/5 x + 3

At this point, some students will start to connect lines being perpendicular to their slopes. While

students will probably not use the correct terminology, perpendicular lines have slopes that are

negative reciprocals, they should see the relationship.

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Main Instruction: Students will be asked to write the equation of a line perpendicular to:

Y = 2x +3. After a sufficient number of answers (at least 3), the entire class will use their

graphing calculators to see if they are right. Make sure students understand that more than one

line can be perpendicular to another. Students will be asked to graph the following equations:

E.) y = 4x       F.) y = 4x + 3         G.) y = 4x – 2          H.) y = -1/4 x     I.) y = -1/4x + 2

Before using their calculators, students should be able to identify which lines are parallel and

which are perpendicular. (Answers to above: E, F, & G are parallel as well as H & I are parallel.

E, F, & G are all perpendicular to H & I.)

Students will use their calculators to verify the class's results.

Closing Activity: Students will create their own set of perpendicular lines and graph it by hand.

Their partner will check it.

Homework: Complete worksheet

1.) – 1/5        2.) 4

3.) Yes, they are perpendicular because their slopes are negative reciprocals.

4.) answers will vary, but must have a slope of –2

5.) C. neither

6.) parallel line must have slope of 3, perpendicular line must have slope of –1/3

7.)Perpendicular lines have slopes that are negative reciprocals

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Perpendicular Lines                                   Name _____________________________

Mr. Swiech                                            Date _________

1.) What is the negative reciprocal of 5? _______

2.) What is the negative reciprocal of –1/4? ______

The following equations are graphed below:            y = -3x + 5 (blue)     y = 1/3x (red)

3.) Are the 2 lines perpendicular? __________         Why? _____________

4.) Write the equation of a line perpendicular to Y = _ x + 4          _________________

5.) What is the relationship between the following lines: y = 2x + 3       y=_x–2

a.) parallel           b.) perpendicular              c.) neither

6.) Write the equation of one line parallel to the equation and one line perpendicular to the
equation: Y = 3X

Parallel Line ____________________                    Perpendicular Line ____________________

7.) State the relationship between perpendicular lines:

______________________________________________________________________________

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