# Investigating Liner Equations Using Graphing Calculator

**Overview:**

Investigating Linear Equations unit consists of 6 graphing activities designed
to

help students explore and learn the concept of linearity using graphing
calculator,

an assessment rubric, and a self-evaluation form. These activities are not meant

to substitute but supplement the chapter on graphing linear equations.

**Time:**

Each activity takes 1-2 class periods.

**Requirements:**

• Students should have the basic knowledge of pre-algebra math concepts,

know about the four quadrants, ordered pairs, plotting points, and

functions; know the meaning of slope and x- and y-intercepts; for activity

#3, students should have mastered solving equations in two variables.

• Teachers should have the knowledge and skills of using the graphing

calculators. Students learn best when teacher demonstrate how to use the

graphing calculator.

• Teacher should prepare and give out handouts with instructions related to

the specific calculator in use. For example, Texas Instruments, Casio or

Sharp calculators are commonly used. In addition there is the Mackintosh

graphing calculator whose program can be downloaded into the class

computers.

**Abstract:**

The emphasis in this unit is on developing the slope-intercept form of the
linear

equation. In the first three activities, the student explores and learns about
the

slope and y-intercept of a line graph by graphing and seeing many graphs.

By activity 4 the student can write the equation of a given graph and check the

result on the calculator. Activity 5 and 6 are real-world applications.

Activity 6 however applies the concept of linearity to scatter plot. students
collect

data of weight versus height of their family members. Make a scatter plot, and

use the line of best fit to interpolate and extrapolate. The teacher guide the

students in using the graphing calculator to check their work.

**Objectives:**

This unit is designed to help the tactile and visual learners in my inclusive
8^{th}

grade algebra class, learn and understand the concept of slope and linear

equations, and how the concept of linearity is applied in real world situations.

• Using the graphing calculator and interactive worksheet activities the

student will load a function into the calculator and immediately see its

graph.

• By graphing different lines, the student will see similarities and differences

in the graphs that lead to specific conclusions based on what they see.

• By answering the questions on the worksheet, the student will compare,

analyze, and make generalizations about the graph. .

• Providing these experiences, the student will begin to see how different

coefficients (slope) affect the shape of the graph.

• By examining the graphs they see, students will identify the x- and yintercepts

of the graph.

• By looking at a line graph, the student will figure out the equation of the

line in the slope-intercept form.

• Having students play with graphing calculators is fun. Students love fun. It

makes learning a desirable rather than hateful experience.

• By using the graphing calculator students engage most of their senses in

the learning process: touching with their fingers (kinesthetic), seeing

(visual), thinking and reasoning (cognetive), and articulating their thoughts

with their partners (auditory).

• Hence, by providing such experiences the teacher makes learning

equitable to all students in the classroom.

**Algebra 1 CA Standards:**

• Standard 5.0 – Students solve multistep problems, including word

problems, involving linear equations. (activities 3 and 4).

• Standard 6.0 – Graph a linear equation and compute the x- and yintercept

(activity 2).

• Standard 7.0 , 8.0 – Understand the slope for use in the point-slope

formula and for understanding parallel lines and pependicular lines

(activities 1, 2, 3).

**National Board Standards:**

• NB Standard I - Commitment to All Students:

"Accomplished mathematics teachers value and acknowledge the individuality

and worth of each student; … they demonstrate these beliefs by providing all

students equitable and complete access to mathematics".

• NB Standard VI - Learning Environment

“Accomplished mathematics teachers create stimulating, caring, and inclusive

environments. They develop communities of involved learners in which students

….work independently and collaboratively, and value mathematics.”

• NB Standard VIII - Technology and Instructional Resources:

"Accomplished mathematics teachersare knowledgeable about and, where

available, use current technologies and other resources to promote student

learning in mathematics."

**Relationship between ETP and my Fellowship:**

**• Math in the work place at Intel
**

• Working at Intel was a very rich and inspiring experience. I was a member

of a team working on optimizing WIP (Work In Progress) delivery to

stations based on process flow and geographical location of work stations

in the Factory (Factory Layout). This kind of work involved a good

knowledge of math in both analyzing statistical data and reading and

intrerpreting graphs. So, I chose a topic for my ETP related to graphs –

graphing linear functions, to teach students the concept of linearity

between two variables; a topic that most students find difficult to

understand in the middle school.

**• Technology in the work place at Intel**

Technology becomes an essential part of learning now-a-days. Hardwares,

softwares, automated machines, all are incorporated to enhance learning,

training, communication, research, development, production, and sales at Intel.

When technology is used to aid instruction in the classroom it enhances the

teaching proces and optimises learning because it will reach not only the
auditory

learner but also the visual and tactile learner. So, I chose to use the
technology

inbeded in the graphng calculator so students play with equations and see the

result on their graphs.

**• Well structured programs for optimal yield at Intel.**

As a company, Intel is highly structured and this is reflected in its programs
and

activities. I chose well structured interactive activities for my ETP to help my

students learn the concept of linear relationships step by step and understand

the process and its reasoning before drawing conclusions.understanding the

process will ensure good results.

**• On going research and development thriving for Excellence.**

Intel engineers and administrators continuosly monitor and assess work in

progress to assure high quality production and optimal results. they invest in

research as a means for development: a pathway to excellence.

So by continually monitoring and assessing students learning and achievement

and working on areas that needs developing we can optimise the outcome of our

teaching.

**Materials/ Resources Needed:**

• Graphing calculator

• Graphing calculator guide/ teacher instructions handout

• Student’s Algebra Text Book: Prentice Hall, McDougal Littell, or other.

• Graph papers

**Sources:
**• Texas Instruments TI-83 plus Explorations.

• TI-83 plus Instructions booklet.

• Graphing Calculator Activities – Dale Seymour.

• Prentice Hall Algebra 1.

• Navigating through Algebra – NCTM.

• Math Forum - Ask Dr. Math.url

## Activity 1

Graphing Lines of the Form y = mx

__Objective:__ In this lesson you will see how the value of m affects the graph of a
straight line.

1. Use the graphing calculator to graph each function and complete the table. An

example is done for you.

Function | Value of m |
Sketch | x-intercept | y-intercept | Is the graph the same, steeper, or flatter than the graph of y = x (or y = -x)? |

y = x | 1 | (0,0) | (0,0) | The same as y = x. | |

y = -x | |||||

y = 2x | |||||

y = -2x | |||||

y = 0.5x | |||||

y = -8x | |||||

y = -0.4x | |||||

y = 0.05x |

2. Use the results to answer the following items.

a. What point does every graph in exercise 1 have in common? ___________________

b. Does the value of m affect the location of the x- or y-intercept?
__________________

c. If the graph lies in quadrants I and III, then m is (positive, negative).
Circle one answer

d. If the graph lies in quadrants II and IV, then m is (positive, negative).
Circle one answer

e. If m is positive, predict what will happen to the graph as m gets larger.
____________

_____________________________________________________________________

f. If m is negative, predict what will happen to the graph as ImI (absolute
value of m)

increases.

_____________________________________________________________________

g. Make a conjecture about the graph when m = 0.

_____________________________________________________________________

_____________________________________________________________________

Check your prediction by graphing the function on your calculator.

h. Summarize the role of m in the graph of y = mx. _____________________________

_____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

3. For each of the following, write an equation of a line that fits the
characteristics. Verify

your answers with the graphing calculator.

a) A straight line in quadrants I and III steeper than y = 3x.

Equation: _____________________________________

b) A straight line in quadrants II and IV flatter than y = -x

Equation; ___________________________________

c) A straight line with the graphs shown below.

Equation: _________________________ Equation:
______________________

d) A straight line that lies between the graphs of y = 3.5x and y = 1.5x.

Equation: ____________________________