This document is a mathematics lesson on solving problems involving linear functions. It contains 4 practice problems. Problem 1 has students solve for the number of wallets to be sold to make a Php 30 profit and express the profit function in terms of wallets sold. Problem 2 deals with the cost of manufacturing shoes. Problems 3 has students model the number of math problems Cassandrea solves each day as a linear function and use it to determine how many problems she will solve on specific days. The document concludes by providing an asynchronous learning activity for students to complete.

1. MATHEMATICS 8
Quarter 2 Week 5
SolvingProblemsInvolving
LinearFunctions
MR. CARLO JUSTINO J. LUNA
MALABANIAS INTEGRATED SCHOOL
Angeles City

2. 2
Learning Competency
➜ Solve problems
involving linear
functions. (M8AL-IIe-
2)

3. Linear
Functions
Linear functions exhibit many real-life situations. It is
widely used in economics, science, engineering and
many everyday applications. Businesses allow them
to determine the increase or decrease of sales.
Doctors can help them in determining the amount of
dosage of a certain medicine for a specific age.
Linear functions help us model any real-world
3

4. 1. How many wallets must be sold to
have a profit of Php 30?
2. How much profit will Mikaela make if
2 wallets were sold?
3. Express the function 𝑃 in terms of 𝑛.
Problem 1

5. 1. How many wallets must be sold to
have a profit of Php 30?
5 wallets
must be sold to
have a Php 30
profit.
Problem 1

6. 2. How much profit will Mikaela make if
2 wallets were sold?
Mikaella will
make a profit of
Php 15
if 2 wallets were
sold.
Problem 1

7. 3. Express the function 𝑃 in
terms of 𝑛.
(0, 5) and 4, 25
𝑦 − 𝑦1 =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
𝑥 − 𝑥1
𝑦 − 5 =
25 − 5
4 − 0
𝑥 − 0
𝑦 − 5 =
20
4
𝑥
𝑦 − 5 = 5𝑥
𝑦 = 5𝑥 + 5
5𝑥 − 𝑦 = −5
Choose any two points from the graph.
Use the Two-Point form in solving for
the linear function.
Substitution
Simplify
Simplify
Slope-intercept form
Standard form
Problem 1

8. Problem 2
The Shoe Factory formulated an
equation 𝑃(𝑛) = 500𝑛 + 70 which
represents the number of
manufactured shoes (𝑛) and the cost
of manufacture (𝑃).
a. What is the cost of manufacturing 40
shoes?
b. If the cost of manufacturing shoes is
Php 7,570, how many shoes are
manufactured?
c. What is the cost of manufacturing 10
8

9. Problem 2
The Shoe Factory formulated an equation 𝑃(𝑛) = 500𝑛 + 70 which
represents the number of manufactured shoes (𝑛) and the cost of
manufacture (𝑃).
a. What is the cost of manufacturing 40 shoes?
9
Answer:
Let 𝑛 = number of manufactured shoes
𝑃 = cost of manufacture shoes
Equation: 𝑃 𝑛 = 500𝑛 + 70
𝑛 = 40
𝑃 𝑛 = 500𝑛 + 70
𝑃 40 = 500 40 + 70
𝑃 40 = 20,000 + 70
𝑷 𝟒𝟎 = 𝟐𝟎, 𝟎𝟕𝟎
Therefore, the cost of manufacturing 40 shoes is 𝑷𝒉𝒑 𝟐𝟎, 𝟎𝟕𝟎.

10. Problem 2
The Shoe Factory formulated an equation 𝑃(𝑛) = 500𝑛 + 70 which
represents the number of manufactured shoes (𝑛) and the cost of
manufacture (𝑃).
b. If the cost of manufacturing shoes is Php 7,570, how many shoes are
manufactured?
10
Answer:
𝑃(𝑛) = 7,570
𝑃 𝑛 = 500𝑛 + 70
7,570 = 500𝑛 + 70
7,570 − 70 = 500𝑛
500𝑛 = 7,500
𝒏 = 𝟏𝟓
Therefore, the cost of manufacturing 15 shoes is Php 7,570.

11. Problem 2
The Shoe Factory formulated an equation 𝑃(𝑛) = 500𝑛 + 70 which
represents the number of manufactured shoes (𝑛) and the cost of
manufacture (𝑃).
c. What is the cost of manufacturing 10 shoes?
11
Answer:
𝑛 = 10
𝑃 𝑛 = 500𝑛 + 70
𝑃 10 = 500 10 + 70
𝑃 10 = 5,000 + 70
𝑷 𝟏𝟎 = 𝟓, 𝟎𝟕𝟎
Therefore, the cost of manufacturing 10 shoes is 𝑷𝒉𝒑 𝟓, 𝟎𝟕𝟎.

12. 12
Problem 3
Cassandrea decides to start solving math
problems in preparation of the upcoming MTAP.
She started answering 5 problems in day 1, 9
problems in day 2, 13 problems in day 3 and so
on.
a. Present your answer in a table until the 6th day.
b. Write a linear function in slope-intercept form to
represent the given problem.
c. How many problems Cassandrea need to
answer on the 10th day?
d. In what day does Cassandrea need to solve 33

13. 13
Problem 3
Cassandrea decides to start solving math problems in
preparation of the upcoming MTAP. She started answering 5
problems in day 1, 9 problems in day 2, 13 problems in day
3 and so on.
a. Present your answer in a table until the 6th day.
Answer:
Day (𝒙)
Number of
Problems
(𝒚)
+𝟒 +𝟒
1
5
2
9
3
13
4 5 6
17 21 25
+𝟒 +𝟒 +𝟒

14. 14
Problem 3
Cassandrea decides to
start solving math
problems in preparation of
the upcoming MTAP. She
started answering 5
problems in day 1, 9
problems in day 2, 13
problems in day 3 and so
on.
b. Write a linear function
in slope-intercept form
to represent the given
Answer:
(1, 5) and 2, 9
𝑦 − 𝑦1 =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
𝑥 − 𝑥1
𝑦 − 5 =
9 − 5
2 − 1
𝑥 − 1
Choose any two points from the
graph.
Use the Two-Point form in solving
for the linear function.
Substitution
Simplify
Simplify
Simplify
Apply Addition Property of Equality
Slope-intercept form
𝑦 − 5 =
4
1
(𝑥 − 1)
𝑦 − 5 = 4 (𝑥 − 1)
𝑦 − 5 = 4 𝑥 − 4
𝑦 = 4 𝑥 − 4 + 5
𝒚 = 𝟒 𝒙 + 𝟏

15. 15
Problem 3
Cassandrea decides to start solving math problems in
preparation of the upcoming MTAP. She started answering 5
problems in day 1, 9 problems in day 2, 13 problems in day
3 and so on.
c. How many problems Cassandrea need to answer on the
10th day?
Answer:
𝑥 = 10
𝑦 = 4𝑥 + 1
𝑦 = 4 10 + 1
𝑦 = 40 + 1
𝒚 = 𝟒𝟏
Therefore,
Cassandrea needs
to answer 41
problems on the
10th day.

16. 16
Problem 3
Cassandrea decides to start solving math problems in
preparation of the upcoming MTAP. She started answering 5
problems in day 1, 9 problems in day 2, 13 problems in day
3 and so on.
d. In what day does Cassandrea need to solve 33
problems?
Answer:
𝑦 = 33
𝑦 = 4𝑥 + 1
33 = 4𝑥 + 1
33 − 1 = 4𝑥
4𝑥 = 32
𝒙 = 𝟖
Therefore,
Cassandrea needs
to solve 33
problems on the 8th
day.

17. 17
Asynchronous / Self-Learning Activities
Answer the following:
Quarter 2 Week 5
• What’s In
• What I Can Do
• Assessment
Google Forms link
• https://forms.gle/EMK1ZCbvYgSgMzW
m8

18. MATHEMATICS 8
Quarter 2 Week 5
Thank
you!
MR. CARLO JUSTINO J. LUNA
MALABANIAS INTEGRATED SCHOOL
Angeles City