1. Chapter IV:
Linear
Equation in
Two Variables

2. 4.1 Rectangular Coordinate
System
4.2 Linear Equation in Two
Variables
4.3 Relation and Function
4.4 Graphing Linear Equations
4.5 Writing Equations of Lines

3. Rectangular
Coordinate
System

4. Objectives:
Define terms related to rectangular
coordinate system;
Value the importance of René Descartes
works in plotting points; and
Locate and plot points on the rectangular
coordinate system.

5. Exploration:
The seat plan of Section I-A prepared by Mr. Santos, the adviser, is shown
below.
Gail
Ryan
Sophia Danielle
Ariel
Shaila
Connie
Rose
Faye
Sedrick
Johanna
John Carl
Paula
Alcas
Denisse Jobelle
Carla
Ayie
Aaron
Jerome
Kirsten
Alice
Edward
Rubie
Aida
Veilant
Brian
Ben
Nina
Mae
Jacob
Gerald Gertude Xavier
Teacher’s Table
Cathy

6. Exploration:
Gail
______
Ariel
(1 , 4)
Rose
______
Sedrick
______
Gerald
______
Ryan
______
Shaila
______
Faye
______
Johanna
(2 , 2)
Gertude
______
Teacher’s Table
Sophia
______
Connie
______
Ayie
______
Edward
______
Xavier
______
Danielle
______
Alcas
______
Aaron
(4 , 3)
Rubie
______
Ben
______
Cathy
______
Denisse
______
Jerome
______
Aida
______
Nina
______
John Carl
(6 , 5)
Jobelle
______
Kirsten
______
Veilant
______
Mae
______
Paula
______
Carla
______
Alice
______
Brian
______
Jacob
(7 , 1)

7. Exploration:
Gail
Ryan
(1 , 5)
(2 , 5)
Ariel
Shaila
(1 , 4)
(2 , 4)
Rose
Faye
(1 , 3)
(2 , 3)
Sedrick Johanna
(2 , 2)
(1 , 2)
Gerald Gertude
(1 , 1)
(2 , 1)
Teacher’s Table
Sophia Danielle Cathy John Carl
(6 , 5)
(3 , 5)
(4 , 5)
(5 , 5)
Connie
Alcas Denisse Jobelle
(3 , 4)
(4 , 4)
(5 , 4)
(6 , 4)
Ayie
Aaron Jerome Kirsten
(3 , 3)
(4 , 3)
(5 , 3)
(6 , 3)
Edward Rubie
Aida
Veilant
(3 , 2)
(4 , 2)
(5 , 2)
(6 , 2)
Xavier
Ben
Nina
Mae
(3 , 1)
(4 , 1)
(5 , 1)
(6 , 1)
Paula
(7 , 5)
Carla
(7 , 4)
Alice
(7 , 3)
Brian
(7 , 2)
Jacob
(7 , 1)

8. QUESTIONS:
Can you see any pattern in the number pairs
written against each student’s name done by
Mr. Cruz? Describe the pattern.
Did Mr. Cruz use the pairs of numbers (2 , 3)
and (3 , 2) to refer to the same seat? If not,
who occupied the seat numbered (2 , 3) and
(3 , 2)?

9. Cartesian Plane or x-y Plane
A Cartesian Plane or x-y Plane (in honor of Rene Descartes) is
made up of two perpendicular number lines (coordinate axes), one is
horizontal (x-axis) and the other is vertical (y-axis), whose point of
intersection is called the origin.
The horizontal line is
called the x-axis or the
abscissa and the vertical line
is called the y-axis or the
ordinate. The two axes divide
the plane into four area called
as
quadrants
that
are
numbered
in
a
counterclockwise direction.

10. RENÉ DESCARTES
René Descartes (1596-1650) is a
French mathematician, philosopher,
and theologian. He was brilliant but
sickly. Thus, his teachers allowed
him to lie in bed in the morning for
rest and reflection. He came up with
many of his philosophical and
mathematical ideas during his
morning meditations, a practice
which he continued throughout his
life.

11. RENÉ DESCARTES
Sometimes the same thing that
makes one person bitter makes
another better. René Descartes, being
sickly, could have resigned himself to a
less remarkable, even miserable life.
Instead, he used those times in his sick
bed to reflect on life and mathematical
relationships, thereby making some of
the most profound discoveries in
mathematics.
Reflect on your life. Is there a
“liability” in your life that you could
turn into an asset? What is it?

12. Locate the point
(2 , 3)

13. To graph or plot a point given its
coordinates:
1. Begin at the origin (0 , 0), move to the right or left
along the x-axis using the number indicated by the
absolute value of the first coordinate.
2. From that position on the x-axis, move up or down
using the number indicated by the absolute value
of the second coordinate.
3. Draw a dot to represent the point described by the
coordinates.

14. To determine the coordinates of a
point in the rectangular system:
1. Draw a vertical line passing through the
point and the x-axis. The number associated
to the point on the x-axis is the first
coordinate.
2.Draw a horizontal line passing through the
point and the y-axis. The number associated
to the point on the y-axis is the second
coordinate.

15. Assignment:
1. Study: Rectangular Coordinate System (illustrative
examples 2 and 3)
2. Answer the following questions:
a.If you are to plot (5 , 2) on the Cartesian plane
without actually plotting, where do you think will
the point lie? Give other points that will be located
on the same region. What do you notice? Make a
generalization.
b.How is the signs of the coordinates affect the
location of the point in the plane? Explain.
c. Does (0 , -1) lie on any of the quadrant? Explain.

16. References:
e – Math 8 (K-to-12 Edition) by Oronce et.al., page
127-131, 135
Intermediate Algebra (Explorations and Applications)
by Gladys Nivera, page 119-124
http://www.math-aids.com/Graphing/
http://www.worksheetworks.com/math/geometry/
graphing.html

17. Thank You
That in all things, God may be Glorified!!!