2nd Quarter Session 1 Direct Variation Introduction

2nd Quarter Session 1 Direct Variation INTRODUCTION

Prepared by Emmanuel Sio

Poll

SECTION

• ASSERTIVE

• COURAGE

• ENTHUSIASTIC

• FORGIVING

• JUSTICE

Open Ended

NAME (LAST NAME, FIRST NAME, MIDDLE INITIAL)

SESSION 1

DIRECT VARIATION

Poll

The more time I drive (at a constant rate), the more distance I cover. (Mas mahabang oras ka nagmamaneho, mas malayo ang nararating)

• AGREE

• DISAGREE

Poll

(In a computer shop)The more hours you play online games, the more money you pay. (Mas matagal kang naglalaro online, mas mataas ang babayaran mo)

• Agree

• Disagree

Poll

If you increase a recipe for more people, the more of ingredients you need. (Kung mas madami ang taong akkain, kinakailangan mo din ng mas madaming sangkap sa iyong linuluto)

• Agree

• Disagree

Poll

• Agree

• Disagree

DIRECT VARIATION

Direct variation is a relationship between two variables such that if one variable changes, the other variable also changes in proportion to the first. Specifically, if the value of one variable increases, the value of the other also increases. Likewise, if the value of one variable decreases, the value of the other also decreases.

Direct Variation

-tumutukoy sa relasyon ng 2 variable kung saan kapag tumaas o lumaki ang isang variable tatas at lalaki din ang kabilang variable at kung bumaba o kumaunti naman ang isang variable pagbaba din o pagliit ang magiging epekto nito sa kabila.

EXAMPLE:

• The time a teacher spends in checking test papers to the number of students. (Mas madami kang checheckan na papel mas mahabang oras din ang kailangan mo.)

• The distance an airplane flies to the time travelling (Mas malayo ang pupuntahan , mas mahabang oras ang magugugol)

EXERCISE 1

Determine if the given situation is an example of direct variation.

Multiple Choice

The fare of a passenger to the distance d of his destination.

• Direct Variation

• Not Direct Variation

Explanation

Ang relasyon ng Fare o pamasahe sa Distance o distansya ay DIRECT VARIATION.

TATAAS ang halaga ng pamasahe mo kapag TUMAAS ang bilang ng distansya o malayo ang linakbay mo.

BABABA naman ang halaga ng pamasahe kapag MABABA lang ang bilang ng distansya o malapit lang ang linakbay mo.

Multiple Choice

The cost of fish to its weight in kilograms

• Direct Variation

• Not Direct Variation

Multiple Choice

The number of hours to finish a job to the number of persons working.

• Direct Variation

• Not Direct Variation

Explanation

Hindi siya direct variation kasi Kung MADAMI kayong taong gagawa ng isang trabaho MAS MALIIT na oras ang kailangan niyo.

TANDAAN: DIRECT VARIATION PAREHAS ANG EPEKTO NG 2 VARIABLE.

KUNG TUMAAS ANG ISA DAPAT TUMAAS DIN ANG KABILA.

KAPAG BUMABA DAPAT BUMABABA DIN ANG KABILA.

Multiple Choice

The number of persons sharing a buko pie to the size of the slices of the pie.

• Direct Variation

• Not Direct Variation.

Multiple Choice

An employee’s salary to the number of days he has worked.

• Direct Variation

• Not Direct Variaton

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.

EXAMPLE 1

The fare F of a passenger varies directly as the distance d of his destination.

ANSWER: F=kd

EXAMPLE 2

The cost C of fish varies directly as its weight w in kilograms.

ANSWER: C=kw

EXAMPLE 3

An employee’s salary S varies directly as the number of days d he has worked.

ANSWER: S=kd

EXAMPLE 4

The area A of a square varies directly as the square of its side s.

ANSWER: A=ks²

EXAMPLE 5

The distance D travelled by a car varies directly as its speed s.

ANSWER: D=ks

Exercise 2

Determine the equation for the following statements.

Multiple Choice

The length L of a person’s shadow at a given time varies directly as the height h of the person.

• L=kh

• H=kL

• L=k/h

• H=k/L

Multiple Choice

The cost of electricity C varies directly as the number of kilowatt-hour consumption l.

• I=kC

• C=kI

• C=k/I

• L=k/C

Multiple Choice

The area (A) of a square varies directly as the square of a side (s).

• A=ks

• A=ks²

• S=kA

• S=kA²

Open Ended

The weight W of an object is directly proportional to its mass m.

Open Ended

The area A of a triangle is proportional to its height h.

Thank you for Participating in Session 1

NEXT: SESSION 2 DIRECT VARIATION PART 2 (COMPUTATIONS)