Alg II 2­2 Direct Variation ­ End.notebook
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August 18, 2016
Direct Variation
A direct variation function is an equation where the ratio of y to x is constant.
y = kx or y/x = k
Where k is the constant of variation or ratio of all pairs of coordinates (x, y).
All direct variation equations go through the origin (0, 0).
Example 1 ­ Identifying Direct Variation From Tables
For each function, determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
A.
B.
C.
D.
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Alg II 2­2 Direct Variation ­ End.notebook
August 18, 2016
Example 2 ­ Identifying Direct Variation From Equations
For each function, determine whether y varies directly with x. If so, find the constant of the variation.
A. 3y = 7x
B. 7y = 14x + 7
C. y = 4x2
Example 3 ­ Using a Proportion to Solve a Direct Variation
y varies directly with x.
A. If y = 9 when x = ­15, what is y when x = 21?
B. If y = 5 when x = ­3, what is x when y = ­1?
C. If y = 15 when x = 3, what is y when x = 12?
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Alg II 2­2 Direct Variation ­ End.notebook
August 18, 2016
Example 4 ­ Using Direct Variation to Solve a Problem
A. A salesperson's commission varies directly with sales. For $1,000 in sales, the commission is $85. What is the commission for $2,300 in sales?
B. 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?
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