Direct Variation

1. DIRECT VARIATION
MATHEMATICS 9

2. The local government of Barangay Talahib
Pandayan launches a recycling campaign of
waste materials to schools in order to raise
students’ awareness of environmental protection
and the effects of climate change. Every kilogram
of waste materials earns points that can be
exchanged for school supplies and grocery
items. Paper, which is the number one waste
collected, earns 5 points for every kilo.
LET’S RECYCLE!

3. The table below shows the points earned by a Grade
8 class for every number of kilograms of waste paper
collected.
1. What happens to the number of points when the
number of kilograms of paper is doubled? tripled?
2. How many kilograms of paper will the Grade 8
class have to gather in order to raise 500 points?
Write a mathematical statement that will relate
the two quantities involved.

4. Using his bicycle, Jericho 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.
HOW STEEP IS ENOUGH!

5. 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?
3. How will you be able to find the distance
(without the aid of the table)? Write a
mathematical statement to represent the
relation.
4. What mathematical operation did you apply
in this case? Is there a constant number
involved? Explain the process that you have
discovered.

7. 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.

8. Your skill in recognizing patterns and knowledge
in formulating equations helped you answer the
questions in the previous activities. For a more
detailed solution of problems involving direct
variation, let us see how this is done.
 If y varies directly as x and y = 24 when x = 6,
find the variation constant and the equation of
variation.
 If x varies directly as y and x = 35 when y = 7,
what is the value of y when x = 25?

9. A. Write an equation for the following statements:
1. The fare F of a passenger varies directly as the distance
d of his destination.
2. The cost C of fish varies directly as its weight w in
kilograms.
3. An employee’s salary S varies directly as the number of
days d he has worked.
4. The area A of a square varies directly as the square of
its side s.
5. The distance D travelled by a car varies directly as its
speed s.
IT’S YOUR TURN!

10. B. Determine if the tables and graphs below
express a direct variation between the variables. If
they do, find the constant of variation and an
equation that defines the relation.
IT’S YOUR TURN!

11. C. Write an equation where y varies directly as x.
1. y = 28 when x = 7
2. y = 30 when x = 8
3. y = 200 when x = 300
D. In each of the following, y varies directly as x.
Find the values as indicated.
4. If y = 12 when x = 4, find y when x = 12
5. If y = -18 when x = 9, find y when x = 7
6. If y = -3 when x = -4, find x when y = 2
IT’S YOUR TURN!

12. Cite real life situations that show
direct variation.
LET’S ASSIMILATE!