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Indirect Variation What is it and how do I know when I see it?
Definition: Y  varies indirectly as  x  means that  y  =  where  k  is the constant of variation. (Another way of writing this is k = xy)  In other words: *  As X increases in value, Y decreases or * As X decreases in value, Y increases.
Examples of Indirect Variation: Note: X increases, 4, 6, 8 And Y decreases. 12, 8, 6 What is the constant of variation of the table above? Since y =  we can say  Therefore: 4•12=k or k = 48 6 •8 =k or k = 48 6 • 8=k or k =48 Note k stays constant. y = 48/x is the equation! X Y 4 12 6 8 8 6
Examples of Indirect Variation: Note: X decreases, 30, 15, 5 And Y increases. 5, 10, 15 What is the constant of variation of the table above? Since y =  we can say  Therefore: 30 • 5=k or k = 150 15 • 10=k or k = 150 5 • 30=k or k =150 Note k stays constant.  y = 150/x is the equation! X Y 30 5 15 10 5 30
What is the constant of variation for the following indirect variation?  ,[object Object],[object Object],[object Object],[object Object],X Y 1 9 3 3 9 1 18 .5
Is this an indirect variation?  If yes, give the constant of variation (k) and the equation. Yes! k = 24 • 2 or 48 Equation? y = 48/x X Y 24 2 12 4 2 24
Is this an indirect variation?  If yes, give the constant of variation (k) and the equation. No! The y-values decrease, but then increase! The k values are also different! X Y 7 5 15 2 20 2.5
Which is the equation that describes the following table of values?  ,[object Object],[object Object],[object Object],[object Object],1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Answer Now X Y 50 4 20 10 10 20
Using Indirect Variation to find unknowns (y = k/x) Given that y varies indirectly with x, and y = 12 when x=4,  Find y when x = 12.  HOW???  2 step process 1. Find the constant variation k = xy or k = 12 • 4 = 48  k=48 2. Use y = k/x. Find the unknown (y). y=48/12  y= 4 Therefore: Y =4 when X=12 X Y 4 12 12 ?
Given that y varies indirectly with x, and y = 100 when x=25, Find x when y = 500.  HOW???  2 step process 1. Find the constant variation. k = yx or k = 100 • 25  K = 2500 2. Use y = k/x. Find the unknown (x). 500 = 2500/x  x = 5 Therefore: X = 5 when Y = 500 Using Indirect Variation to find unknowns (y = k/x) X Y 25 100 500
Indirect Variation and its graph With indirect variation the equation  is y = k/x Note:  Because one variable is always doing the opposite of the other variable, the graph will never go through….
the ORIGIN!!!!!
The graph of Indirect Variation
Using Indirect Variation to solve word problems Problem: A gas with volume 45 cubic inches is under a pressure that is 75 pounds per square inch. Find the pressure when the volume is 80 cubic inches. Step One :   Find points in table. Step Two:   Find the constant variation and equation: k = xy or k = 45 • 75 = 3375 y =  3375/x Step Three:   Use the equation  to find the unknown. y = 3375/80  y = 42.1875 X (volume) Y (pressure) 45 75 80 ?
Using Indirect Variation to solve word problems Problem: A gas with volume 30 cubic inches is under a pressure that is 40 pounds per square inch. Find the pressure when the volume is 60 cubic inches. Step One:  Find points in table. Step Two:   Find the constant variation. k = xy or k = 30 • 40 = 1200 k = 1200 Step Three:   Use the equation  to find the unknown. y=k/x y = 1200/60 y = 20 X (volume) Y (pressure) 30 40 60 ?
Mini Quiz ,[object Object],[object Object],[object Object],X Y 4 7 6 4  2/3 8 3 ½
Mini Quiz Continued… ,[object Object],[object Object]
Compare and Contrast Direct and Indirect Variation  ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Indirect variation notes

  • 1. Indirect Variation What is it and how do I know when I see it?
  • 2. Definition: Y varies indirectly as x means that y = where k is the constant of variation. (Another way of writing this is k = xy) In other words: * As X increases in value, Y decreases or * As X decreases in value, Y increases.
  • 3. Examples of Indirect Variation: Note: X increases, 4, 6, 8 And Y decreases. 12, 8, 6 What is the constant of variation of the table above? Since y = we can say Therefore: 4•12=k or k = 48 6 •8 =k or k = 48 6 • 8=k or k =48 Note k stays constant. y = 48/x is the equation! X Y 4 12 6 8 8 6
  • 4. Examples of Indirect Variation: Note: X decreases, 30, 15, 5 And Y increases. 5, 10, 15 What is the constant of variation of the table above? Since y = we can say Therefore: 30 • 5=k or k = 150 15 • 10=k or k = 150 5 • 30=k or k =150 Note k stays constant. y = 150/x is the equation! X Y 30 5 15 10 5 30
  • 5.
  • 6. Is this an indirect variation? If yes, give the constant of variation (k) and the equation. Yes! k = 24 • 2 or 48 Equation? y = 48/x X Y 24 2 12 4 2 24
  • 7. Is this an indirect variation? If yes, give the constant of variation (k) and the equation. No! The y-values decrease, but then increase! The k values are also different! X Y 7 5 15 2 20 2.5
  • 8.
  • 9. Using Indirect Variation to find unknowns (y = k/x) Given that y varies indirectly with x, and y = 12 when x=4, Find y when x = 12. HOW??? 2 step process 1. Find the constant variation k = xy or k = 12 • 4 = 48 k=48 2. Use y = k/x. Find the unknown (y). y=48/12 y= 4 Therefore: Y =4 when X=12 X Y 4 12 12 ?
  • 10. Given that y varies indirectly with x, and y = 100 when x=25, Find x when y = 500. HOW??? 2 step process 1. Find the constant variation. k = yx or k = 100 • 25 K = 2500 2. Use y = k/x. Find the unknown (x). 500 = 2500/x x = 5 Therefore: X = 5 when Y = 500 Using Indirect Variation to find unknowns (y = k/x) X Y 25 100 500
  • 11. Indirect Variation and its graph With indirect variation the equation is y = k/x Note: Because one variable is always doing the opposite of the other variable, the graph will never go through….
  • 13. The graph of Indirect Variation
  • 14. Using Indirect Variation to solve word problems Problem: A gas with volume 45 cubic inches is under a pressure that is 75 pounds per square inch. Find the pressure when the volume is 80 cubic inches. Step One : Find points in table. Step Two: Find the constant variation and equation: k = xy or k = 45 • 75 = 3375 y = 3375/x Step Three: Use the equation to find the unknown. y = 3375/80 y = 42.1875 X (volume) Y (pressure) 45 75 80 ?
  • 15. Using Indirect Variation to solve word problems Problem: A gas with volume 30 cubic inches is under a pressure that is 40 pounds per square inch. Find the pressure when the volume is 60 cubic inches. Step One: Find points in table. Step Two: Find the constant variation. k = xy or k = 30 • 40 = 1200 k = 1200 Step Three: Use the equation to find the unknown. y=k/x y = 1200/60 y = 20 X (volume) Y (pressure) 30 40 60 ?
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