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MATHEMATICS 8
PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
ACTIVITY
DISCUSSION
QUARTER 2 WEEK 1

DIFFERENTIATING LINEAR
INEQUALITIES AND LINEAR
EQUATIONS IN TWO
VARIABLES
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
ACTIVITY
DISCUSSION
QUARTER 2 WEEK 1
MARC JOSHUA C. CLARETE, LPT
SUBJECT TEACHER

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY
After going through this lesson, you are expected to:
1.distinguish the linear inequalities in two
variables from linear equations in two
variables;
2.translate mathematical phrases into
mathematical statements of linear
equations and inequalities in two
variables; and
3.cite real life situations that can be
represented by linear equations and
inequalities in two variables.

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY
ACTIVITY: EXPRESS ME
Directions: Express the following linear
equations in two variables into its standard
form + = .
𝐴𝑥 𝐵𝑦 𝐶
1. 2x = y – 3
2. y = -4x + 7
3. 2y = 8x – 9
4. x = 2y + 4
5. x – 3y – 7 = 0
2x – y = -3
4x + y = 7
8x – 2y = 9
x – 2y = 4
x – 3y = 7

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY
ACTIVITY: BE MY PARTNER
Directions: Match the verbal statement in column A to the
mathematical statement in Column B.

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY Differentiating Linear Inequalities and Linear Equations in Two Variables
Equations and inequalities are two
significant concepts in mathematics that
are related but are different in some ways.
Inequality is a mathematical
statement where one expression is not
equal to another. It uses the symbols , ≤
, ≥, ≠. While
𝑜𝑟 equation uses the
symbol “=” indicating that the value of
the expressions from both sides are
equal.

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Definition:
A linear equation in
two variables is written
in the standard form of
+ + = 0,
𝐴𝑥 𝐵𝑦 𝐶
where , , and
𝐴 𝐵 𝐶
are real numbers and
the coefficients of 𝑥
and , represented
𝑦
by and
𝐴 𝐵
respectively, are not
equal to zero.
LINEAR INEQUALITY
Definition:
A linear inequality in
two variables is formed
when symbols other
than equal to, such as
greater than or less
than are used to relate
two expressions, and
two variables are
involved.

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Standard Form:
𝐴𝑥 + = C
𝐵𝑦
LINEAR INEQUALITY
Standard Form:
𝐴𝑥 + <
𝐵𝑦 𝐶
𝐴𝑥 + >
𝐵𝑦 𝐶
𝐴𝑥 + ≥
𝐵𝑦 𝐶
𝐴𝑥 + ≠
𝐵𝑦 𝐶
𝐴𝑥 + ≤ C
𝐵𝑦

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Translating Verbal
Statements to
Mathematical
Statements:
1. The sum of a
number and
𝑥
a number y is
24.
𝑥 + = 24
𝑦
LINEAR INEQUALITY
Translating Verbal
Statements to
Mathematical
Statements:
1. The sum of a
number and
𝑥
a number is
𝑦
greater than
24.
𝑥 + > 24
𝑦

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Translating Verbal
Statements to
Mathematical
Statements:
2. A number x
decreased by is
𝑦
24.
–
𝑥 𝑦 = 24
LINEAR INEQUALITY
Translating Verbal
Statements to
Mathematical
Statements:
2. A number 𝑥
decreased by a
number is less
𝑦
than 24.
–
𝑥 𝑦 < 24

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Translating Verbal
Statements to
Mathematical
Statements:
3. The sum of
twice a number 𝑥
and thrice a
number is 30.
𝑦
2 + 3 = 3
𝑥 𝑦 0
LINEAR INEQUALITY
Translating Verbal
Statements to
Mathematical
Statements:
3. The sum of
twice a number 𝑥
and thrice a
number is at
𝑦
least 30.
2 + 3 ≥ 30
𝑥 𝑦

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Translating Verbal
Statements to
Mathematical
Statements:
4. Twice a number
decreased by
𝑥
thrice a number 𝑦
is 30.
2 – 3 = 30
𝑥 𝑦
LINEAR INEQUALITY
Translating Verbal
Statements to
Mathematical
Statements:
4. Twice a number
decreased by
𝑥
thrice a number 𝑦
is at most 30.
2 – 3 ≤ 30
𝑥 𝑦

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Characteristics of the
graph:
Straight line
LINEAR INEQUALITY
Characteristics of the
graph:
Plane or half-
plane

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Sample Graphs:
LINEAR INEQUALITY
Sample Graphs:

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Graphical Solutions:
set of points on
the line
LINEAR INEQUALITY
Graphical Solutions:
region of points
bounded by a line

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
LINEAR EQUATION
Effects when multiplied
or divided by a
negative integer:
Equality symbol is
not changed
For example:
3 – 2 = 6
𝑥 𝑦
LINEAR INEQUALITY
Effects when multiplied
or divided by a
negative integer:
Direction of the
inequality symbol
is reversed
For example:
3 − 2 > 6
𝑥 𝑦

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY
ACTIVITY: DORA D’ EXPLORER
The class will be divided into four groups. Each group
will begin at a different station simultaneously. Each
station will have a unique activity that the group
must complete before moving on to the next. After
completing a station, the group will proceed to the
next one in a clockwise direction. Each group will
rotate until they complete all four stations. You have
20minutes to finish all the station. The first group to
complete all four stations in the given time will
receive 10 points, 2nd
(8pts.), 3rd
is 7pts, and 4th
is
(5pts.). The scores from all stations will be added,
along with the bonus points based on the group’s
finishing position.

PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY
ACTIVITY: DORA D’ EXPLORER
The class will be divided into four groups. Each group will begin
at a different station simultaneously. Each station will have a
unique activity that the group must complete before moving on to
the next. After completing a station, the group will proceed to the
next one in a clockwise direction. Each group will rotate until
they complete all four stations. You have 20minutes to finish all
the station. The first group to complete all four stations in the
given time will receive 10 points, 2nd
(8pts.), 3rd
is 7pts, and 4th
is
(5pts.). The scores from all stations will be added, along with the
bonus points based on the group’s finishing position.
Station 1: Sort me well!
Station 2: Name Me!
Station 3: What am I?
Station 4: Shall I Stay or Be the Other Way?

THANK YOU!
PRAYER
OBJECTIVES
WHAT’S
IN
WHAT’S
NEW
DISCUSSION
ACTIVITY

�ݺ�ߣ

MATHematics 8 second quarter first module.pptx

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