2.2 Direct Variation
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2.2 DIRECT VARIATION
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DIRECT VARIATION
Direct Variation functions have equations of the form y = kx, where k is the constant of variation and does not equal 0, x represents the input values, and y represents the output values. Many types of physical phenomena exhibit direct
variation, such as rates (miles per gallon, miles per hour, cost per pound)
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DIRECT VARIATION
The graphs of direct variation functions always pass through the origin.
The formula says that the ratio of all output-input pairs equals the constant of variation, k. This is used to determine whether a function is a
direct variation function.
yk
x
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IDENTIFYING DIRECT VARIATION FROM TABLES
1. Determine whether y varies directly with x, by checking the ration of all output-input pairs
2. Identify the constant of variation by simplifying
3. Plug k into
1 2
1 2
... n
n
y y y
x x x
yk
x
y kx
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EXAMPLE
For each function, determine whether y varies directly with x. If so, what is the constant of variation, and the function rule?
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EXAMPLE
For each function, determine whether y varies directly with x. If so, what is the constant of variation, and the function rule?
![Page 7: 2.2 Direct Variation](https://reader033.fdocuments.us/reader033/viewer/2022061414/553ab79555034657228b45c7/html5/thumbnails/7.jpg)
IDENTIFYING DIRECT VARIATION FROM EQUATIONS
1. Solve for y.2. If it looks like this: then it is a
direct variation y kx
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EXAMPLE
For each function, determine whether y varies directly with x. If so, what is the constant of variation?
![Page 9: 2.2 Direct Variation](https://reader033.fdocuments.us/reader033/viewer/2022061414/553ab79555034657228b45c7/html5/thumbnails/9.jpg)
EXAMPLE
For each function, determine whether y varies directly with x. If so, what is the constant of variation?
7 14 7y x
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USING A PROPORTION TO SOLVE A DIRECT VARIATION
1. Set up a proportion:
2. Fill in what you know
3. Solve for the missing piece
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EXAMPLE
Suppose y varies directly with x, and y = 9 when x = -15. What is y when x = 21?
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EXAMPLE
Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?
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GRAPHING DIRECT VARIATION EQUATIONS The graph of a direct variation function is
always a line through the origin.
To graph a direct variation: Complete a table of values Plot the points
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EXAMPLE
What is the graph of each direct variation equation?
3
4y x
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EXAMPLE
What is the graph of each direct variation equation?
2y x
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USING A DIRECT VARIATION TO SOLVE A PROBLEM
The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contain 200 Calories, how many Calories are in 70 grams of cheese?