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- 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. What is the constant of variation for the following indirect variation? <ul><li>-9 </li></ul><ul><li>9 </li></ul><ul><li>-1/9 </li></ul><ul><li>1/9 </li></ul>X Y 1 9 3 3 9 1 18 .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. Which is the equation that describes the following table of values? <ul><li>y = -2/x </li></ul><ul><li>y = 2/x </li></ul><ul><li>y = -200/x </li></ul><ul><li>y = 200/x </li></ul>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
- 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….
- 12. the ORIGIN!!!!!
- 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 ?
- 16. Mini Quiz <ul><li>Is this an indirect variation? If yes, give the constant of variation (k) and the equation. </li></ul><ul><li>Given that y varies indirectly with x, and y =8 when x=1.5, Find y when x = 3. </li></ul><ul><li>Find an equation of indirect variation where y varies indirectly as x. One pair of values is y = 15 when x = 8. </li></ul>X Y 4 7 6 4 2/3 8 3 ½
- 17. Mini Quiz Continued… <ul><li>4. The time (t) required to do a certain job varies inversely as the number (n) of people working (assuming all work at the same rate). It takes 4 hours for 20 people to wash and wax the floors in a building. Find the equation of variation. </li></ul><ul><li>5. It takes 16 hours for 2 people to resurface a gym floor. How long would it take 6 people to do the job? </li></ul>
- 18. Compare and Contrast Direct and Indirect Variation <ul><li>With respects to </li></ul><ul><li>The equation </li></ul><ul><li>How to find the constant of variation </li></ul><ul><li>The graphs </li></ul><ul><li>Others? </li></ul>

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