This document discusses joint variation, which refers to a situation where two or more quantities vary together such that if one quantity changes, the other quantities also change by the same factor or proportion. The document provides examples of translating joint variation statements into mathematical equations and vice versa. It also asks learners to compose two real-life examples that illustrate joint variation and to translate several given joint variation statements into mathematical equations.

1. JOINT VARIATION
Illustrating and
Translating Joint
Variation

2. LEARNING OBJECTIVES:
1. Illustrates situations that involves
joint variation.
2. Translate joint variation
statement into mathematical
equation and vice versa.

3. LEARNING TARGETS:
K - Identify joint variation.
U -Translate joint variation into
mathematical equation and vice versa.
D -Compose statements that illustrate
joint variation.

4. Review:
Translate the statement below into mathematical
equation.
The area (A) of the wall to be painted varies directly
to the number of workers (w).
Atmospheric pressure (P) varies inversely as the
altitude (h).
Question:
What type of variations are shown in the situation?
Why?

5. Suppose we have this new statement.
The area (A) of wall to be painted varies jointly to
the number of workers (w) and the pail (p) of
paints needed to do the task.
1. Compare the first and second situation.
2. How can you translate the situation into
mathematical equation?

6. Based from the given situation a
while ago, translate the statement
into mathematical equation.
a. The area (A) of wall to be painted
varies jointly to the number of workers
(w) and the pail (p) of paints needed to
do the task.

7. JOINT VARIATION
The statement “a varies jointly as b and
c” means a = kbc, or 𝑘=𝑎𝑏𝑐 where k is
the constant.
Illustrative example:
Translate the statement
1. The area (A) of a triangle varies jointly as its base (b)
and its altitude (h).
2. The pressure (P) of a gas varies jointly as its density (d),
and its absolute temperature (t).
3. The area (A) of a lot in subdivision varies jointly as the

8. BOARDWORK
Direction: Translate each statement into a mathematical sentence.
Use k as the constant of variation
1. The volume V of a parallelogram varies jointly as the length l,
width w, and its height h.
2. The volume of a cylinder V varies jointly as height h and the
square of the radius r.
3. The heat H produced an electric lamp varies jointly as the
resistance R and the square of the current i.
4. The perimeter P of a rectangle varies jointly as its length l and
width w.
5. The area A of a parallelogram varies jointly as the base b and
altitude h.
6. The force F applied to an object varies jointly as mass m and the
acceleration a.

9. ANSWERS:
1. V= klwh
2. V= kh𝑟2
3. H=kR𝑖2
4. P=kLw
5. A=khl
6. F=kma

10. COMPOSE TWO REAL – LIFE
SITUATIONS THAT
ILLUSTRATE JOINT
VARIATION.

11. ACTIVITY
A. Translate the following joint variation statement.
1. The volume V of a pyramid varies jointly as the area of the square root of the base b
and the altitude h.
2. The appropriate length S of a rectangular beam varies jointly as the square of width w
and the square root its depth d.
3.The electrical voltage V varies jointly as the current I and the resistance r.
4. The weight (W) of a circular disc varies jointly as the square of its radius (r) and its
thickness (h)
5. P varies jointly as q and r.
6. V varies jointly as l, w, and h
7. The volume of a cylinder (V) varies jointly as its height (h) and the square of the radius.
8. The electrical voltage (V) varies jointly as the current (I) and the resistant (R).
9.-10. Compose two real – life situations that illustrate joint variation.

12. THANK YOU!!!!