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# Indirect variation notes

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### Indirect variation notes

1. 1. Indirect Variation What is it and how do I know when I see it?
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 12. the ORIGIN!!!!!
13. 13. The graph of Indirect Variation
14. 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. 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. 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. 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. 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>