Tarlac State University
COLLEGE OF TEACHER EDUCATION
CENTER OF DEVELOPMENT
Lucinda Campus, Tarlac City
Tel. No. (045) 493-0182; Fax No. (045) 982-0110
Re-accredited Level IV by the Accrediting Agency of Chartered Colleges and Universities of
the Philippines (AACUP), Inc.
Detailed Lesson Plan | Mathematics 8
I.
II.
III.
A. Content Standards
● The learner demonstrates understanding of key concepts of factors of polynomials,
rational algebraic expressions, linear equations and inequalities in two variables,
system of linear equations and inequalities in two variables and linear functions.
B. Performance Standards
● The learner is able to formulate real-life problems involving factors of polynomials,
rational algebraic expressions, linear equations and inequalities in two variables,
system of linear equations and inequalities in two variables and linear functions and
solve these problems accurately using a variety of strategies.
C. Most Essentials Learning Competencies
● The learner writes the linear equation 𝐴𝑥 + 𝐵𝑥 = 𝐶 in the form of 𝑥 = 𝑥𝑥 + 𝑥
and vice versa.
D. Learning Competencies
Objectives:
At the end of this lesson, the students should be able to:
● Differentiate standard form of linear equations from slope-intercept form.
● Write the linear equation 𝐴𝑥 + 𝐵𝑥 = 𝐶 in the form of 𝑥 = 𝑥𝑥 + 𝑥 and vice
versa.
Subject Matter
Topic: Patterns and Algebra
Sub. Topic: Writing the linear equation 𝐴𝑥 + 𝐵𝑥 = 𝐶 in the form of 𝑦 = 𝑥𝑥 + 𝑥 and vice
versa.
References: Grade 8 Mathematics Quarter 1-Module 9
Procedures
Day 3
Teacher’s Activity
A. Preparation
- Prayer
- Greetings
- Checking of Attendance
B. Review
Before we proceed to our discussion for
today, let us first have a short review. What
did we discussed last meeting?
Student’s Activity
(Student will press the raise hand button)
Teacher, we discussed the linear equation in
two variables.
What is a linear equation in two variables?
(Student will press the raise hand button)
If A, B and C are real numbers and A and B
are not equal to 0, it is called a Linear
equation in two variables. The standard form
of linear equation in two variables is 𝐴𝑥 +
𝐵𝑦 = 𝐶.
Very Good! What else did we discussed last
meeting?
(Student will press the raise hand button)
Teacher, we discussed slope-intercept form.
Very good! We also discussed slopeintercept form. And what about the slopeintercept form, can you share to the class
what are the things you remember?
(Student will press the raise hand button)
Teacher, the slope-intercept form is written
in the form of 𝑦 = 𝑚𝑥 + 𝑏, where m is the
slope and b is the y-intercept and they are
both real numbers.
Very Good! A linear equation in two
variable is written in the standard form of
𝐴𝑥 + 𝐵𝑦 = 𝐶, where A, B and C are real
numbers and A and B must not equal to
zero. While slope-intercept form is written
in the form of 𝑦 = 𝑚𝑥 + 𝑏, where m is the
slope and b is the y-intercept and they are
both real numbers.
Let us have a review first if you
remembered the difference of standard form
in linear equation in two variables and
slope-intercept form. I will show on the
screen different equations and classify
whether it is a standard form of linear
equation in two variables or slope-intercept
form.
(The teacher presents the equation on the
screen one-by-one)
3x – y = 7
y = 5x – 2
y = -x + 9
3x + 6y = 12
−3𝑥
y= 4 +1
y=
2𝑥
3
+5
Correct answer:
Standard form
Slope-intercept form
Standard form
Standard form
Standard form
Slope intercept form
It seems like you understood our topic last
meeting. Do you have any questions?
Clarifications?
Okay! Now, please pass your assignments
to the center aisle and forward. Do not
stand, just pass the paper, okay?
C. Motivation
Before we proceed to our next topic, let us
have an activity first.
That’s the end of our activity.
D. Presentation of the Lesson
E. Lesson Proper
The equation of the form 𝑥𝑥 + 𝑥𝑥 = 𝑥
can be written in the form 𝑥 = 𝑥𝑥 + 𝑥 and
vice versa.
Remember:
Standard Form: 𝑥𝑥 + 𝑥𝑥 = 𝑥, where
A, B, and C are elements of real numbers, A
and B are not equal to 0.
Slope-intercept form: 𝑥 = 𝑥𝑥 + 𝑥,
where m is the slope and b is the y-intercept,
m and b are elements of real numbers.
In rewriting standard form of a linear
equation to slope-intercept form, let us
isolate the variable y in the left side of the
equation.
example 1:
rewrite the equation -4x + y = 12 in slopeintercept form.
-4x + y = 12
-4x + y + 4x = 12 + 4x (Addition Property
of Equality)
y + (-4x + 4x) = 12 + 4x (Associative
Property for Addition)
y + 0 = 12 + 4x
(Additive Inverse)
y = 12 + 4x
(Identity Property
for Addition)
y = 4x + 12
(Commutative
Property of Equality/ Slope-Intercept Form)
None, Teacher!
Yes, Ma’am
(The student will pass their assignments)
example 2:
Rewrite the equation y = -3x + 9 in the
standard form.
y = -3x + 9
y + 3x = - 3x + 9 + 3x (Addition Property
of Equality)
y + 3x = (-3x + 3x) + 9 (Associative
Property for Addition)
y + 3x = 0 + 9
(Additive Inverse)
y + 3x = 9
(Identity Property
for Addition)
3x + y = 9
(Commutative
Property for Addition/ Standard Form)
Next example, can anyone rewrite the
equation in the form 𝑥 = 𝑥𝑥 + 𝑥 and
determine the slope and y-intercept.
Correct answer:
solution a:
-3x + y = 9
-3x + y + 3x = 12 + 3x
(The teacher will call someone to answer the of Equality)
y + (-3x + 3x) = 12 + 3x
questions)
Property for Addition)
y + 0 = 12 + 3x
y = 12 + 3x
for Addition)
y = 3x + 12
Property for Addition)
a. -3x + y = 9
b. 20x – 10y = 30
(Addition Property
(Associative
(Additive Inverse)
(Identity Property
(Commutative
➢ The slope is 3 and the y-intercept is
12.
solution b:
20x – 10y = 30
20x – 10y – 20x = 30 – 20x (Addition
Property of Equality)
– 10y + 0 = 30 – 20x
(Additive Inverse)
– 10y = 30 – 20x
(Identity Property
for Addition)
1
1
− 10 (–10y) = − 10 (30 – 20x)
(Multiplication Property of Equality)
y = – 3 + 2x
(Multiplicative Inverse)
y = 2x – 3
(Commutative Property
For Addition)
➢ The slope is 2 and the y-intercept is
-3.
To write slope-intercept form 𝑥 = 𝑥𝑥 + 𝑥
to standard form 𝑥𝑥 + 𝑥𝑥 + 𝑥 = 0, let
𝑥
m= 𝑥, collect all terms on the left side of the
equation and multiply by the denominator B
to get rid of the fraction.
example 4:
Rewrite the following equation in the form
𝑥𝑥 + 𝑥𝑥 = 𝑥.
a. y = -x + 4
2
b. y = 3 𝑥 + 5
solution a:
y = -x + 4
y + x = -x + x + 9 (Additional Property of
Equation)
y + x = (-x + x) + 9 (Associative Property
for Addition)
y+x=0+9
(Additive Inverse)
y+x=9
(Identity Property for
Addition)
x+y=9
(Commutative Property
for Addition/ Standard Form)
How about in letter b, who will transform
slope-intercept form to standard form?
(The teacher will call someone to answer the
question.)
solution b:
y=
2
𝑥+5
3
2
(3)(y) = (3)( 𝑥 + 5) (Multiplication
3
Property of Equality)
6
3y = 𝑥 + 15
(Distributive Property)
3
6
3y = 2x + 15
(Simplified: 3 = 2)
3y + (-2x) = 2x + 15 + (– 2x) (Addition
Property of Equality)
3y + (-2x) = (2x – 2x) + 15 (Associative
Property for Addition
3y + (-2x) = 0 + 15 (Additive Inverse)
3y – 2x = 0 + 15
(Distributive Property)
3y – 2x = 15
(Identity Property for
Addition)
– 2x + 3y = 15
(Commutative Property)
(-1) (– 2x + 3y)=(-1) (15) (Multiplication
Property of Equality)
2x – 3y = –15
(Standard Form)
example 5:
Eli’s mother asked her to buy apple and
orange in the market. Each apple costs ₱ 20
and each orange costs ₱ 10. She was told by
her mother to spend exactly ₱ 50.
a. write an equation in standard form
and rewrite the equation in slope-
intercept form
solution:
let x represent the number of apples
y represent the number of oranges
20x + 10y = 50
20x +10y = 50
20x + 10y – 20x = 50 – 20x (Addition
Property of Equality)
(20x – 20x) + 10y = 50 – 20x (Associative
Property of Addition)
0 +10y = 50 – 20x
(Additive Inverse)
10y = 50 – 20x
(Identity Property for
Addition)
1
1
(10y) = 10 (50 – 20x) (Multiplication
10
Property of Equality)
y = 5 – 2x
(Multiplicative Inverse)
y = – 2x + 5
(Commutative Property)
F. Application
Let us have an activity.
A. Rewrite in the form 𝑥 = 𝑥𝑥 + 𝑥,
then identify the slope and the yintercept.
1. 7x + 4y = 20
2. -4x + 2y = -20
B. Rewrite in the for 𝑥𝑥 + 𝑥𝑥 =
𝑥.
2
1. y – 5 = 3(x – 3)
3
2. y + 8 = 4(x + 4)
correct answer:
A.
1. 7x + 4y = 20
7x + 4y = 20
7x + 4y – 7x = 20 –7x
(7x – 7x) + 4y = 20 – 7x
0 + 4y = 20 – 7x
4y = 20 – 7x
1
1
(4) (4y) = (4) (20 – 7x)
7
y = 5 – 4x
7
y = – 4x + 5
7
➢ the slope is – 4 and the y-intercept
is 5.
2. -4x + 2y = -20
-4x + 2y = -20
-4x + 2y + 4y = -20 + 4x
(-4y + 4y) + 2y = -20 +4x
0 + 2y = -20 +4x
2y = -20 + 4x
1
1
(2)(2y) = (2)(-20 + 4x)
y = -10 + 2x
y = 2x – 10
➢ The slope is 2 and the y-intercept is
-10.
B.
2
3
1. y – 5 = (x – 3)
2
3
y – 5 = (x – 3)
2
y–5=3x-2
2
-3 x + y = -2 + 5
2
–3 x + y = 3
2
(-3) (-3 x + y) = (-3) ( 3)
2x – 3y = -9
3
2. y + 8 = 4(x + 4)
3
y + 8 = 4 (x + 4)
3
y + 8 = 4x + 3
3
- 4x + y = 3 – 8
3
- 4x + y = -5
3
(- 4) (- 4x + y) = (-4) (-5)
3x – 4y = 20
G. Generalization
To sum up the discussion, what have you
learned from today’s discussion?
We learned on how to write the linear
equation 𝐴𝑥 + 𝐵𝑥 = 𝐶 in the form of 𝑥 =
𝑥𝑥 + 𝑥 and vice versa.
IV.
Evaluation
A. Monica collected 2 kg of plastic bottles for their Christmas tree. She plans to collect
an additional 3 ½ kg each week. Complete the table below, and use the mathematical
equation describing the situation in finding the standard form 𝐴𝑥 + 𝐵𝑥 = 𝐶.
No. of weeks (x)
No. of kilograms (y)
V.
Assignment
Prepared by:
Agpawa, Denver Jonn D,
Day, Rejane Mae C.
Espino, Jessa Mae D.
Pring, Tracy Kyla F.
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Student Teacher
Checked by:
Nelvin Nool
Professor