This document discusses direct variation and provides examples of word problems involving direct variation. It begins by defining direct variation as "y varies directly as x" and lists learning objectives about solving direct variation problems, applying the concept to real-life situations, and appreciating direct variation. Several word problems then follow involving situations like a pineapple farmer's pay depending on the number of pineapples harvested, the cost of papayas depending on their weight, and money raised at an event depending on attendance. These problems are worked out and more examples are given involving topics like gasoline used for travel, circumference of circles, voltage in electric circuits, and direct variation in amounts of water and pressure.

1. Direct Variation
“y varies directly as x”

2. a.Solve problems involving direct
variation
b. Apply the concepts learned about
direct variation in solving verbal
problems
c. Appreciate the concept of direct
variation in real-life situation

3. Mang Tony is a worker in a
pineapple plantation. During
harvest season, the owner of the
plantation pays him Php 7.00 for
every 5 pineapples he will
gather.

5. In the following table, c is the
amount he received from the
owner and n is the number of
pineapples.

6. Mang Tony is a worker in a
pineapple plantation. During
harvest season, the owner of
the plantation pays him Php
7.00 for every 5 pineapples he
will gather.

7. a.What mathematical statement can
relate between the two quantities n
and c?
b. What is the constant of variation?
Formulate the mathematical equation.
c. Graph the relation.

8. d. How much would Mang Tony
receive if he will be able to
harvest 500 pineapples?
e. What product can be
produced using pineapple?

11. d. c = Php 700
e. pineapple juice;
pineapple jam;
pineapple candy; etc.

12. Group Work

13. The cost (c) of a ripe papaya
varies directly as weight (w).
If a 2-kg papaya costs Php
45.00, how much should a 3-
kg papaya cost?

15. The amount of money raised during
JS Promenade Night varies directly
as the number of attendees. The
amount of money raised for 5
attendees was Php 1000.00. How
much money will be raised for 124
attendees?

17. Nomer uses 20 liters of
unleaded gasoline to travel
200 kilometers, how many
liters of gasoline will he use
on a trip of 700 kilometers?

18. Solution: If the distance(d)
traveled varies directly as the
amount of unleaded
gasoline (u) consumed, then

20. The circumference of a circle
varies directly as its diameter. If
the variation constant (k) is
what is the circumference of a
circle whose diameter is 12 cm?
18 cm? 25 cm?

22. Express an equation where k is
the constant of variation: the
voltage (V) in an electric circuit
varies directly as the current (I).
If I = 5 when V = 110, find V
when I = 12.

24. a. What equation do
we use in solving direct
variation word
problems?

25. b. Can we apply the
different concepts learned
about direct variation to
real life-situations?

26. a. If c varies directly as the square root of d, and
c = 16 when d = 64, find c when d = 324.
b. A student earns Php 280.00 for a 5 hour shift
on his summer job. The amount of money he
earns varies directly to the number of hours
worked. Find the constant k, and the amount of
money he will earn for an 8-hour shift.
Exercise # 2.4

28. 1. The number of kilograms of water K
in a human body is directly proportional
to its total weight W. A man who weighs
87 kg contains 58 kg of water. If
Marcelo weighs 72 kg, how many
kilograms of water does he contain?
Assignment

29. 2. The pressure p at the bottom of a
swimming pool varies directly as the
depth d of the water. If the pressure
is 125 Pascal when the water is 2
meters deep, find the pressure
when it is 4.5 meters deep.
Assignment

31. 1. K = 48.24 kg
2. 281.25 Pascal
Assignment