1. Direct Variation

2. Objectives At the end of this presentation, the students should be able to: Know what is direct variation; Be familiarize with the formulas in solving problems regarding the topic; Apply the necessary steps to answer correctly the activities given.

3. When two variable quantities have a constant (unchanged) ratio, their relationship is called a direct variation. It is said that one variable "varies directly" as the other.

4. The formula for direct variation is y = kx, where k is the constant of variation. "y varies directly as x" Solving for k: (y = numerator; x = denominator)

5. The graph for Direct Variation is

7. Example #1: If y varies directly as x, find the constant of variation and the value of x when y is 12, if y is 4 when x is 6. First step: Using the given, identify the missing variables. k= ? x= ? y= 12 ; y= 4 x= 6

8. Second step: Substitute the values to the formula given. y= 4 x=6 k= ? k= y/x k= 6/4 k= 2/3  Constant of variation y= 2/3 x (Equation of Variation)

9. k= 2/3 y= 12 x= ? y= kx 12= 2/3x 36= 2x 2 2 x= 18

10. Example #2: The weekly salary a woman earns, S, varies directly as the number of hours, h, which she works. Express this relation as a formula. Answer: S = hk or ( where k is the constant)

11. Example #3: If y varies directly as x, find the percent increase in y if x is increased by 25%. Answer: y=kx y=1.25kx ~*~ y is increased by 25% ~*~

12. Analyze, Think and Solve!!!

13. The following slides contains some challenging and burdensome problems for you to deal with… GOODLUCK!!!

14. PROBLEM #1: If (a+b) varies directly as (a-2b), prove that b varies directly as a. [HINT: Solve for b in terms of a and explain the result.]

15. PROBLEM #2: Determine the constant of proportionality in the following direct variations and find the unknown value of the indicated variable. a.If y varies directly as x, and y=10 when x=5, find y when x=15.

16. PROBLEM #3: A machine can make 6405 screws in 3 hours. How many screws can it make in 8 hours?

18. Kristine Mae M. Guerra Frances Lira V. Calabia Jude Carlo G. Bolivar