direct and inverse variations
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Direct and Inverse Variations. Direct Variation. Which of these tables models direct variation? If so, write an equation. NO. Tell if the following graph is a Direct Variation or not. Yes (straight line through the origin!). No. No. No. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/1.jpg)
Direct and Inverse
Variations
![Page 2: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/2.jpg)
Direct Variation
![Page 3: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/3.jpg)
Which of these tables models direct variation? If so, write an equation.
NO
![Page 4: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/4.jpg)
Tell if the following graph is a Direct Variation or not.
No Yes
(straight line through the origin!)
No No
![Page 5: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/5.jpg)
example:If y varies directly as x and y = 10 as x = 2.4, find x when y =15.
10
2.4
15
x10x = 36
x=3.6
![Page 6: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/6.jpg)
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Cross multiply: 96 = 2ySolve for y. 48 = y.
12
2y
8
![Page 7: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/7.jpg)
The Weight (V) of an object on Venus varies directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 150 lb on Earth weigh on Venus?
150(106) = 120y15900 = 120y
132.5 pounds =y
![Page 8: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/8.jpg)
Inverse Variation
Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down.
The values of x and y always multiply to give the same value.
![Page 9: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/9.jpg)
Graphs of inverse variation…
![Page 10: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/10.jpg)
Which of these tables models indirect variation? If so, write an equation.
NO
![Page 11: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/11.jpg)
Inverse Variation
With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.
x1y1 = x2y2
![Page 12: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/12.jpg)
Inverse Variation
If y varies inversely with x and y = 12 when x = 2, find y when x = 8.
x1y1 = x2y2
2(12) = 8y 24 = 8y y = 3
![Page 13: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/13.jpg)
Inverse VariationIf y varies inversely as x and x = 18 when y = 6, find y when x = 8.
18(6) = 8y 108 = 8y y = 13.5
![Page 14: Direct and Inverse Variations](https://reader035.vdocument.in/reader035/viewer/2022062221/5681449c550346895db14a6b/html5/thumbnails/14.jpg)
In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long?
10=6x
1.67 lbs=x