Aguila Glenn M.

Grade - 9
Direct
Variance
Definitions and Examples
Prepared by Glenn M. Aguila

Prayer
Dear God,
May we, through your blessings,
ADD purity to the world,
SUBTRACT evil from our lives,
MULTIPLY Your Good News, and
DIVIDE Your gi s and share them with
others.
Fill our minds with learning,
Fill our classrooms with peace.
Amen.
Objectives
At the end of the lesson, learners should be able to:
Define Solve Relate
Define accurately Solve problems Relate the concept

direct variation, involving direct of direct variation
variation correctly, to one’s life.
and
Activity 1:
A-pair,
Dis-a-pair
Direction:
● Ten random students will be chosen using the “fishbowl method”.

● They will choose a random card from the deck and are tasked to find their
partners.
● There are two types of cards; the statement cards (or the cause cards),
and the icon cards (or the effect cards).
● One pair must contain a cause and an effect card.
● You will only given 5 - 7 minutes to do the activity.
● After you find your partner, your teacher will ask you one-by-one why you
think your partner is the right one for you (for your scenario).
Statement
Cards
Icon
Cards
Answer the following questions:
1) How do you find the activity?

2) Can you relate in any of the situations above?
3) Do you think playing cards, are generally good? If yes, then
give a situation when it turns bad, if no then explain why.
4) What do you think is the cause and effect of playing cards
as a fun game? How about when gambling?
Activity 2:
Jericho the Biker
Jericho decided to ride his bike, he now travels a distance of 10
kilometers per hour on a steep road. The table shows the distance he has
travelled at a particular length of time.
Time (hr) 1 2 3 4 5
Distance (km) 10 20 30 40 50
Time (hr) 1 2 3 4 5
Distance (km) 10 20 30 40 50
Answer the following questions:

1. What happens to the distance as the length of time increases?
2. Using this pattern, how many kilometers would he have travelled in 8

1/2 hours? How about in 11 hours?
3. What mathematical operation did you apply in this case? Explain the
process that you have discovered.
Watch and Learn
Watch and take notes of the important
details you will find on the video about
Direct Variation.
· https://study.com/learn/lesson/direct-variation-equation.html
After watching the video;
1) What did you learn from the video?
2) Which word/s was/were mentioned

that you think defined direct variation?
3) Can you give one example that was

mentioned? What do you think is the
connection of it into the direct variation?
4) What is the formula that was · https://study.com/learn/lesson/direct-variation-equation.html
mentioned? What is it for?

Direct
Variation
Direct Variation
There is direct variation whenever a situation produces pairs of
numbers in which their ratio is constant. The statements: “y varies
directly as x” “y is directly proportional to x” and “y is proportional to x”
may be translated mathematically as y = kx, where k is the constant of
variation.
For two quantities, x and y, an increase in x causes an increase in y

as well. Similarly, a decrease in x causes a decrease in y.
In the previous activity, a-pair, dis-a-pair, when the area of the wall
to be painted increases, the paint needed also increases. On the other
hand, on the video we watched before, when the temperature of the
atmosphere decreases, so as the people who are willing to buy the ice
cream.
If the distance d varies directly as the time t, then the relationship

can be translated into a mathematical statement as d=kt, where k is
the constant of variation. Likewise, if the distance d varies directly as
the rate r, then the mathematical equation describing the relation is
d=kr.
Another instance is in the activity, Jericho the Biker, the variation
statement that is involved between the two quantities is d=10t. In this case,
the constant of variation is k=10.
Using a convenient scale, the graph of the relation d=10t is a line.
The graph below describes a direct variation of the form y = kx

For a more detailed solution of problems involving direct variation, let us see how
this is done.
Example 1. If y varies directly as x and y = 24 when x = 6, find the variation constant and
the equation of variation.
Solution:
a. Express the statement “y varies directly as x” as y = kx.
b. Solve for k by substituting the given values in the equation.
y = kx
24 = 6k
k = 24/6
k=4
Therefore, the constant of variation is 4.
c. Form the equation of the variation by substituting 4 in the statement,
y = kx.
y = 4x
Example 2. The table below shows that the distance d varies directly as the time t. Find
the constant of variation and the equation which describes the relation.
Time (hr) 1 2 3 4 5
Distance (km) 10 20 30 40 50
Solution: Since the distance d varies directly as the time t, then d = kt.
Using one of the pairs of values, (2, 20), from the table, substitute the values of d and t in
d = kt and solve for k.
d = kt
20 = 2k
k = 20/2
k = 10
Therefore, the constant of variation is 10.
Form the mathematical equation of the variation by substituting 10 in the statement
d = kt.
d = 10t
We can see that the constant of variation can be solved if one pair of values of x and
y is known. From the resulting equation, other pairs having the same relationship can be
obtained. Let us study the next example
Example 3. If x varies directly as y and x = 35 when y = 7, what is the value of y when

x = 25?
Solution 1. Since x varies directly as y, then the equation of variation is in the form x = ky.
Substitute the given values of y and x to solve for k in the equation.
35 = k(7)
k = 35/7
k=5
Hence, the equation of variation is x = 5y.
Solving for y when x = 25,
25 = 5y
y = 25/5
y=5
Hence, y = 5.
Solution 2.
Since x/y is a constant, then we can write k = x/y . From here, we can
establish a proportion such that:
x₁/y₁ = x₂ y₂ where x₁ = 35, y₁ = 7 and x₂ = 25.
Substituting the values, we get

35/7 = 25/y₂
5 = 25/y₂
y₂ = 25/5
y₂ = 5
Therefore, y = 5 when x = 25.
Can you
give
examples?
Group
Activity
Differentiated Activities: Students will be divided into 3
groups and will be given a different roles and tasks. Students will
be given 7 - 10 minutes preparation, these task are as follows:
Group 1: Dramatization
The group will be tasked to prepare a skit presenting a minimum

of 3 to 4 scenarios that shows the concepts of direct variation.
Group 2: Verbal-Linguistic Learners
The group will be tasked to prepare a 3 to 4 stanza poem about

the concepts of direct variation.
Group 3: Musical
The group will be tasked to prepare a 3 to 4 verse song with the

lyrics telling something about the concepts of direct variation.
Students will be assessed using the rubric below:
Group Member Very Frequently (3) Occasionally (2) Never (1)
Contribute ideas
Focuses on the
task
Ensures the
quality work
Works with others
Total Score ___/12

Generalization:
● Direct Variation is the type of variation that always have the two
values/variables proportional.
● The ratio of a direct variation is always constant.
● In translating “y varies directly as x”, y must always stay on the left side of
the equation, while x must be placed on the right side together with the k
(where k is the constant of a variation), becoming “y=kx”
● In translating “x varies directly as y”, x must always stay on the left side of
the equation, while y must be placed on the right side together with k
(where k is the constant of a variation), becoming “x=ky”
● When the term k is missing the formula y=kx will become k=x/y
Do you
have any
questions?
“The results you achieve will be in direct
proportion to the effort you apply.”
—Denis Waitley
Let’s Check
your ability!
In your notebook or scratch paper, answer the following individually
A. Direction: Read the questions carefully and choose the letter of the
correct answer. You may write the questions or answer only
1. Which of the following best describes the direct variation?

a. The two quantities are proportional
b. The two quantities are not proportional
c. The two quantities can be x or y
d. The two quantities can be indirectly proportional
2. In direct variation, when a one quantities increases, the other one ___.
a. Increases
b. Decreases
c. Depreciates
d. Constant
3. How can you mathematically translate, “s is proportional to t”?
a. t=ks
b. k=ts
c. s=kt
d. k=st
4. (1) In direct variation, if x increases the y decreases. (2)“y varies directly as x” can
be translated to y=kx
a. Both statement are correct
b. Both statement are wrong
c. The first statement is correct, and the second is wrong
d. The first statement is wrong, and the second is correct
5. Write an equation of , “the length L of a person’s shadow at a given time varies
directly as the height H if the person”
a. k=LH
b. H=kL
c. k=HL
d. L=kH
B. Direction: In each of the following, y varies directly as x. Find the
following.
1. If y = 12 when x = 4, find y when x = 12
2. If y = -18 when x = 9, find y when x = 7
3. If y = 81 when x = 9, find y when x = 4
Let’s Check!
Assignment:
Answer the following problem, show your solutions.
1. Jessie uses 20 liters of gasoline to travel 200 kilometers, how
many liters of gasoline will he use on a trip of;
a. 700 kilometers?
b. 900 kilometers?
c. 1,000 kilometers?
2. If y varies directly as x, and y = 2.5 when x = .25,

find y when x = .75
Thanks!
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Grade - 9

Prepared by Glenn M. Aguila

Define Solve Relate

Define accurately Solve problems Relate the concept

● Ten random students will be chosen using the “fishbowl method”.

1) How do you find the activity?

Answer the following questions:

2. Using this pattern, how many kilometers would he have travelled in 8

2) Which word/s was/were mentioned

3) Can you give one example that was

4) What is the formula that was · https://study.com/learn/lesson/direct-variation-equation.html

mentioned? What is it for?

For two quantities, x and y, an increase in x causes an increase in y

If the distance d varies directly as the time t, then the relationship

The graph below describes a direct variation of the form y = kx

Example 3. If x varies directly as y and x = 35 when y = 7, what is the value of y when

x₁/y₁ = x₂ y₂ where x₁ = 35, y₁ = 7 and x₂ = 25.

Substituting the values, we get

The group will be tasked to prepare a skit presenting a minimum

Group 2: Verbal-Linguistic Learners

The group will be tasked to prepare a 3 to 4 stanza poem about

The group will be tasked to prepare a 3 to 4 verse song with the

Group Member Very Frequently (3) Occasionally (2) Never (1)

Works with others

Total Score ___/12

1. Which of the following best describes the direct variation?

2. If y varies directly as x, and y = 2.5 when x = .25,

CREDITS: This presentation template was created by Slidesgo, and

Please keep this slide for attribution

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