DIRECT VARIATION.pptx

Math 9 Direct Variation quarter 2

1. MATHEMATICS 9 – QUARTER 2

2. ___ I R ___ C ____ ( adj ) - extending or moving from one place to another by the shortest way without changing direction or stopping . V A ___ I ____ T ___ O ___ is defined by any change in some quantity due to change in another fairly simple relationships or formulas GUESS THE WORD?

3. 4 TYPES OF VARIATION DIRECT VARIATION INVERSE VARIATION JOINT VARIATION COMBINED VARIATION

4. IF WASTE PAPERS WERE RECYCLED REGULARLY, IT WOULD HELP PREVENT THE CUTTING OF TREES, GLOBAL WARMING AND OTHER ADVERSE EFFECTS THAT WOULD DESTROY THE ENVIRONMENT. DO YOU AGREE? “WILL A DECREASE IN PRODUCTION OF PAPER CONTRIBUTE TO THE DECREASE IN THE NUMBER OF TREES BEING CUT?”

5. DIRECT VARIATION

6. OBJECTIVES i llustrates situations that involve direct variation Translate into variation statement a relationship involving direct variation between two quantities given by a table of values , a mathematical equation , a graph and vice versa Solve problems involving direct variation

7. Direct variation - is a type of proportionality wherein one quantity directly varies with respect to a change in another quantity. This implies that if there is an increase in one quantity then the other quantity will experience a proportionate increase. Similarly, if one quantity decreases then the other quantity also decreases.  is a linear relationship hence, the graph will be a straight line . This can be expressed in mathematical statement of equation as y = kx , where is the constant of variation or constant of proportionality. These statements can be: “ y varies directly as x” “ y is directly proportional to x” and “ y is proportional to x”  

8. EXAMPLES The area of the wall is directly proportional to the amount of paint used to cover it. The amount of food to eat in a family is directly proportional to the number of household members. The cost of life insurance is directly proportional to the age of the insured person.

9. Go to page 198 of your book.

10. Show that distance (d) varies directly as time (t) Draw the graph of d against t Write an equation showing the relationship between d and t. How far Kyle travelled after 8 hour and 10.5 hours?

11. A. Show that distance (d) varies directly as time (t) TIME (t) hour 1 2 3 4 5 DISTANCE (d) km 10 20 30 40 50 Ratio = = 10 =10 = 10 = 10 = 10 TIME (t) hour 1 2 3 4 5 DISTANCE (d) km 10 20 30 40 50

12. B. Draw the graph of d against t

13. C. Write an equation showing the relationship between d and t.

14. Oral Participation Write an equation of the following statements. The distance D travelled by a car varies directly as its speed s . The weight W of an object is directly proportional to its mass s . An employee’s salary S varies directly as the number of days d he has worked. 2. If x varies directly as y and x = 35 when y = 7, what is the value of the constant of variation? Write the equation of variation. 3. If y = 12 when x = 4, find y when x = 12. 4. If y = -18 when x = 9, find y when x = 7.

15. Find the constant of variation for the given table of values.

16. Given the graph, find the constant of variation and equation of variation.

17. QUIZ Write an equation for the following statements. The fare F of a passenger varies directly as the distance d of his destination. The cost C of fish varies directly as its weight w in kilograms. The cost of electricity C varies directly as the number of kilowatt-hour consumption n . The area A of a triangle is proportional to its height h . The length L of a person’s shadow at a given time varies directly as the height h of the person.

18. B. Given the table of values, find the constant of variation and equation of variation. C. Given the graph, find the constant of variation and equation of variation. x 1 2 3 4 y 3 6 9 12 1 2 3 4 5 50 40 30 20 10 y x

19. D. Find the constant of variation and write an equation of variation. y = 28 when x = 7 y = 30 when x = 8