This document discusses direct variation and provides examples to illustrate it. Direct variation is a relationship between two quantities where a change in one produces a change in the other. The key points are: - Direct variation can be expressed as "y varies directly as x" or "y is directly proportional to x" and is represented by the equation y=kx, where k is the constant of variation. - An example is given of paint needed (y) for classrooms (x) where y=5x, showing the direct relationship through a table of values. - Students are instructed to draw a graph from a similar table to visually represent the direct variation relationship between paint and number of classrooms.

2. I. OBJECTIVES
M9 AL-IIa-1
 Illustrate situations that involve direct
variation.
Solve problems involving direct
variation.

3. What is Variation?
Variation is a relationship between
two quantities in which a change in one
quantity produces a change in another
quantity.

4. Situation:
Connecting to a peso wifi (vendo machine.)
Questions:
1. Have you experienced using wifi vendo machine?
2. What did you observe to the time when the amount
you inserted increases?
- The time increases when the amount inserted in the
peso wifi (vendo machine) increases.

5. Group Activity House rules:
 Cooperate with your groupmates.
 Don’t make any noise that can disturb other
groups.
Focus on what have been asked to do.

6. Steps to do
1. Draw a circle with the diameter of 10cm, 20cm and 30cm using the
sticks given.
2. Use the formula 𝐶 = 𝜋𝑑 where C is the circumference, d is the
diameter and 𝜋 = 3.14.
3. Solve for the value of C and complete the table below.
Diameter (d) 10cm 20cm 30cm
Circumference (c)
π

7. Using the table of values.
𝒄 = 𝝅𝒅 𝝅 = 𝟑. 𝟏𝟒
𝒅 = 𝟏𝟎 𝒅 = 𝟐𝟎 𝒅 = 𝟑𝟎
Diameter (d) 10cm 20cm 30cm
Circumference (c)
π (k)
31.4 62.8 94.2
3.14 3.14 3.14

8. 1.What happens to the circumference when the
diameter changes?
2.What can you say about the relationship
between the circumference and the diameter
of the circle?

9. Direct Variation
It is a relationship between two
quantities when one increases the other
quantity also increases; when one quantity
decreases, the other quantity also decreases.

10. These statements can be:
“y varies directly as x”
“y is directly proportional to x”
“y is proportional to x”
Thus, y=kx, where:
y = dependent variable
x = independent variable
k = constant.

11. The amount of paint (p) needed varies directly to
the number of classrooms (c) to be painted. If 5
gallons of paint is used for 1 classroom, how
many gallons of paint needed to paint 4, 6, 8, and
10 classrooms? Use the formula p=k(c). Show
your answers using a table of values.

12. Table of values
Use the formula p=k(c).
Paint (p) = 5
Classroom (c) = 1
Classroom (c) 2 4 6 8
Paint (p)
Constant (k)
10 20 30 40
5 5 5 5

13. Evaluation
Liza bought a watermelon costing php 30.00 per
kilogram. How much it cost if she bought 2, 4, 6, …
kilograms of watermelon? The costs (c) of watermelon
varies directly to the number of kilograms (n) she
bought.
Using the equation c=P(n)
Show your solution using direct variation.
No. of kilograms (n) 2 4 6
Cost (c)

14. Assignment
Using the table of values, draw the graph of the amount of paint
against number of classrooms.
Classroom (c) 2 4 6 8 10
Paint (p) 10 20 30 40 50