Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes...
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Transcript of Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes...
![Page 1: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/1.jpg)
Direct and Inverse
Variations
Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?
![Page 2: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/2.jpg)
Today we will be able to solve and graph Inverse
Variation problems
Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?
5
15=
4x
x=12
This is a direct variation problem. We set them upAs a proportion and solve.
![Page 3: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/3.jpg)
Direct Variation
When we talk about a direct variation, we are talking about a relationship where as x increases, y increases or decreases at a CONSTANT RATE.
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Direct Variation
y1x1
=y2
x2
Direct variation uses the following formula:
![Page 5: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/5.jpg)
Direct Variationexample:
if y varies directly as x and y = 10 as x = 2.4, find x when y =15.
what x and y go together?
![Page 6: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/6.jpg)
Direct VariationIf y varies directly as x and y = 10
find x when y =15.
y = 10, x = 2.4 make these y1 and x1
y = 15, and x = ? make these y2 and x2
![Page 7: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/7.jpg)
Direct Variation
if y varies directly as x and y = 10 as x = 2.4, find x when y =15
10
2.4=
15x
![Page 8: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/8.jpg)
Direct Variation
How do we solve this? Cross multiply and set equal.
10
2.4=
15x
![Page 9: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/9.jpg)
Direct Variation
We get: 10x = 36
Solve for x by diving both sides by
10.
We get x = 3.6
![Page 10: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/10.jpg)
Direct Variation
Let’s do another.
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
Set up your equation.
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Direct Variation
If y varies directly with x and y = 12 when x = 2, find y when x = 8.
12
2=
y8
![Page 12: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/12.jpg)
Direct Variation
Cross multiply: 96 = 2ySolve for y. 48 = y.
12
2=
y8
![Page 13: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/13.jpg)
Inverse Variation
Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. Can you think of an exampleOf this happening?
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Inverse Variation
With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.
x1y1 = x2y2
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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
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Inverse Variation
If y varies inversely with x:
X 4 8 2 x
Y 6 3 y -1
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Inverse Variation
If y varies inversely with x and allProducts =24
X 4 8 2 X=-24
Y 6 3 Y=12 -1
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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
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Graphing inverse variations-the graph is a hyperbola.
xy = c where c is the product of x and y
Ex: xy = 12 then y=
12x
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Example:
If it takes 3 carpenters to frame a house in 8 weeks, how many weeks will it take four carpenters to frame the same house?
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Example:
If it takes 3 carpenters to frame a house in 8 weeks, how many weeks will it take four carpenters to frame the same house?
(3)(8) = (4)(w)W =6
![Page 22: Direct and Inverse Variations Do now: if 5 boxes of salt costs 15 dollars, how much does 4 boxes cost?](https://reader035.fdocuments.us/reader035/viewer/2022062222/5697bffa1a28abf838cc01c8/html5/thumbnails/22.jpg)
Exit ticket
Create an inverse variation problem with your partner and hand it in on an index card for 3 bonus points on your next test!