Chapter IV: Chapter IV: Linear Linear

Equation in Equation in Two VariablesTwo Variables

4.1 Rectangular Coordinate System

4.2 Linear Equation in Two Variables

4.3 Relation and Function4.4 Graphing Linear Equations4.5 Writing Equations of Lines

Rectangular Rectangular Coordinate Coordinate

SystemSystem

Objectives:

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

Exploration:

GailGail RyanRyan SophiaSophia DanielleDanielle CathyCathy John CarlJohn Carl PaulaPaula

ArielAriel ShailaShaila ConnieConnie AlcasAlcas DenisseDenisse JobelleJobelle CarlaCarla

RoseRose FayeFaye AyieAyie AaronAaron JeromeJerome KirstenKirsten AliceAlice

SedrickSedrick JohannaJohanna EdwardEdward RubieRubie AidaAida VeilantVeilant BrianBrian

GeraldGerald GertudeGertude XavierXavier BenBen NinaNina MaeMae JacobJacob

Teacher’s Table

The seat plan of Section I-A prepared by Mr. Santos, the adviser, is shown The seat plan of Section I-A prepared by Mr. Santos, the adviser, is shown below.below.

Exploration:GailGail

____________RyanRyan

____________SophiaSophia____________

DanielleDanielle____________

CathyCathy____________

John CarlJohn Carl(6 , 5)(6 , 5)

PaulaPaula____________

ArielAriel(1 , 4)(1 , 4)

ShailaShaila____________

ConnieConnie____________

AlcasAlcas____________

DenisseDenisse____________

JobelleJobelle____________

CarlaCarla____________

RoseRose____________

FayeFaye____________

AyieAyie____________

AaronAaron(4 , 3)(4 , 3)

JeromeJerome____________

KirstenKirsten____________

AliceAlice____________

SedrickSedrick____________

JohannaJohanna(2 , 2)(2 , 2)

EdwardEdward____________

RubieRubie____________

AidaAida____________

VeilantVeilant____________

BrianBrian____________

GeraldGerald____________

GertudeGertude____________

XavierXavier____________

BenBen____________

NinaNina____________

MaeMae____________

JacobJacob(7 , 1)(7 , 1)

Teacher’s Table

Exploration:GailGail

(1 , 5)(1 , 5)RyanRyan(2 , 5)(2 , 5)

SophiaSophia(3 , 5)(3 , 5)

DanielleDanielle(4 , 5)(4 , 5)

CathyCathy(5 , 5)(5 , 5)

John CarlJohn Carl(6 , 5)(6 , 5)

PaulaPaula(7 , 5)(7 , 5)

ArielAriel(1 , 4)(1 , 4)

ShailaShaila(2 , 4)(2 , 4)

ConnieConnie(3 , 4)(3 , 4)

AlcasAlcas(4 , 4)(4 , 4)

DenisseDenisse(5 , 4)(5 , 4)

JobelleJobelle(6 , 4)(6 , 4)

CarlaCarla(7 , 4)(7 , 4)

RoseRose(1 , 3)(1 , 3)

FayeFaye(2 , 3)(2 , 3)

AyieAyie(3 , 3)(3 , 3)

AaronAaron(4 , 3)(4 , 3)

JeromeJerome(5 , 3)(5 , 3)

KirstenKirsten(6 , 3)(6 , 3)

AliceAlice(7 , 3)(7 , 3)

SedrickSedrick(1 , 2)(1 , 2)

JohannaJohanna(2 , 2)(2 , 2)

EdwardEdward(3 , 2)(3 , 2)

RubieRubie(4 , 2)(4 , 2)

AidaAida(5 , 2)(5 , 2)

VeilantVeilant(6 , 2)(6 , 2)

BrianBrian(7 , 2)(7 , 2)

GeraldGerald(1 , 1)(1 , 1)

GertudeGertude(2 , 1)(2 , 1)

XavierXavier(3 , 1)(3 , 1)

BenBen(4 , 1)(4 , 1)

NinaNina(5 , 1)(5 , 1)

MaeMae(6 , 1)(6 , 1)

JacobJacob(7 , 1)(7 , 1)

Teacher’s Table

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

QUESTIONS:QUESTIONS:

Cartesian Plane or x-y PlaneCartesian 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.

RENÉ DESCARTESRENÉ 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.

RENÉ DESCARTESRENÉ 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?

Locate the point(2 , 3)

To graph or plot a point given its To graph or plot a point given its coordinates: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.

To determine the coordinates of a To determine the coordinates of a point in the rectangular system: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.

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.

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 

Thank You

That in all things, God may be Glorified!!!