Direct and Inverse Variations Direct Variation Which of these tables models direct variation? If so,...
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Transcript of Direct and Inverse Variations Direct Variation Which of these tables models direct variation? If so,...
Tell if the following graph is a Direct Variation or not.
No Yes
(straight line through the origin!)
No No
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
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
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
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.
Inverse Variation
With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.
x1y1 = x2y2
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
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