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Direct Variation

Learn about direct variation and how to solve problems using the direct variation formula. Gain familiarity with the necessary steps to answer activities correctly.

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Direct Variation

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  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

  6. EXAMPLES

  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. A.T.S 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. • 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?

  17. SUBMITTED BY: Kristine Mae M. Guerra Frances Lira V. Calabia Jude Carlo G. Bolivar

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