This document discusses direct variation, which is a relationship between two quantities where one quantity increases as the other increases or decreases, maintaining a constant ratio. The document provides examples of situations that exhibit direct variation, such as distance traveled increasing directly with time. It defines direct variation mathematically and provides formulas. Examples are given of writing direct variation equations and solving for unknown variables. The key aspects of direct variation are explained, such as the constant of variation and using tables and graphs to demonstrate direct variation relationships.

1. DIRECT
VARIATIO
N

2. Objectives

3. At the end of the lesson, the students
will be able to:
a. illustrate situations involving direct
variation;
b. write an equation of direct
variation; and
c. demonstrate direct variation
through tables and graphs

4. AGREE
OR
DISAGREE?
Motivation

5. 1.The more time I drive (at a constant
rate), the more distance I cover.

6. 1.The more time I drive (at a constant
rate), the more distance I cover.
ANSWER:
AGREE

7. 2.If you increase a recipe for more
people, the more ingredients you need.

8. 2.If you increase a recipe for more
people, the more ingredients you need.
ANSWER:
AGREE

9. 3.In a computer shop, the more hours you
play online games, the more money you pay.

10. 3.In a computer shop, the more hours you
play online games, the more money you pay.
ANSWER:
AGREE

11. 4.The more apparels I purchase, the more
money it costs.

12. 4.The more apparels I purchase, the more
money it costs.
ANSWER:
AGREE

13. GROUP
ACTIVITY

15. 1. What do you observed in the
illustration?
2. Is there a relationship between the
number of oranges to its total cost?
3. Have you experience any
difficulties?

16. ABSTRACTION
Direct variation is a relationship
between two quantities, x and y,
where as x increases y also
increases or as y decreases x also
decreases and the ratio between
them is constant or the same for
all given values of the variables.

17. So , if y varies directly as x, then
we say y = kx or k= y/x and k is
called the constant of variation.

18. Things to Remember:
VARIES DIRECTLY
DIRECTLY PROPORTIONAL

19. Formula’s to Remember:
y= kx Direct variation formula
Where, k is the Constant
y= kx y= kx
x
x
= k
y
x
k= y
x
constant formula

20. Example 1
The money(m) you pay varies
directly on the number of
hours(h) you play online games.
If you play 4 hours(h) and paid
P80.00, what is k?

21. Answer:
m=kh m=80, h=4
80=k(4)
4 4
k=40

22. Example 2
The more time I drive (at a constant
rate), the more distance I cover,
therefore the distance(d) I cover varies
directly to the time(t) I drive. If I drive
50m in 5 hours, what is k?

23. Answer:
d = kt d=50, t=5
50= k(5)
5 5
k=25

24. Example 3
The commission (C) of a
salesman varies directly to the
amount of his sales (S). How will
his commission change when
his sales are doubled?

26. Example 4
The table below shows a direction since the
Cost(C) increases as a number of kilos (n)
increases which means the more you buy, the
more it costs. The lesser you buy, the lesser it
costs. Give the translation of the problem.

27. C = k(n)
Find K
ORIGINAL FORMULA
y= kx

28. C= k(n) 200= k(1)
k=200

30. Example 5
Suppose c varies directly as d.
What is c if k=4 and d=6?

31. Answer:
c= kd k=4, d=6
c= (4)(6)
c= 24

32. Example 6
If r varies directly as d and
r = 12 when k= 2 what is d?

33. Answer:
r= kd r=12, k=2
12= (2)d
6=d
2

34. Example 7
When looking at two buildings at the
same time, the length of the buildings’
shadows (s) varies directly as their height (h).
If a 5-story building has a 20 m long shadow,
how many stories high would a building that
has a 32 m long shadow be?

35. Answer:
Therefore the building has
8 stories if the building
has a 32m long shadow.

36. Application

37. ASSESSMENT

38. ASSIGNMENT

39. Thank