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1. For each function, determine whether y varies directly with x. If so, what are the constant of variation and the function rule?

   1. x	3	2	1
      y	− 21 negative 21	− 14 negative 14	− 7 negative 7

   2. x	2	3	6
      y	5	7	13

Problem 2 Identifying Direct Variation From Equations

For each function, determine whether y varies directly with x. If so, what is the constant of variation?

1. 3y = 7x

   Divide each side of the equation 3 y = 7 x 3 y equals 7 x  by 3 to get y = 7 3 x . y equals . 7 thirds , x .  Since you can write the equation in the form y = k x , y equals k x comma  y varies directly with x. The constant of variation is 7 3 . 7 thirds , .

2. 7 y = 14 x + 7 7 y equals 14 x plus 7

   Divide each side of the equation 7 y = 14 x + 7 7 y equals 14 x plus 7  by 7 to get y = 2 x + 1 . y equals 2 x plus 1 .  Since you cannot write the equation in the form y = k x , y equals k x comma  y does not vary directly with x.

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2. For each function, determine whether y varies directly with x. If so, what is the constant of variation?
   1. 5 x + 3 y = 0 5 x plus 3 y equals 0
   2. y = x 9 y equals , x over 9

Problem 3 Using a Proportion to Solve a Direct Variation

Suppose y varies directly with x, and y = 9 y equals 9  when x = − 15 . x equals negative 15 .  What is y when x = 21 ? x equals 21 question mark

9 − 15 = y 21 In a direct variation , y x is constant . 9 ( 21 ) = − 15 ( y ) Write the cross products . 9 ( 21 ) − 15 = − 15 y − 15 Divide each side by − 15. − 12.6 = y Simplify . table with 4 rows and 3 columns , row1 column 1 , 9 over negative 15 , column 2 equals , y over 21 , column 3 cap inadirectvariation . comma , y over x . isconstant . . , row2 column 1 , 9 , open 21 close , column 2 equals negative 15 , open y close , column 3 cap writethecrossproducts . . , row3 column 1 , fraction 9 , open 21 close , over negative 15 end fraction , column 2 equals . fraction negative 15 y , over negative 15 end fraction , column 3 cap divideeachsideby . minus 15. , row4 column 1 , negative , 12.6 , column 2 equals y , column 3 cap simplify , . , end table

So y is − 12.6 negative , 12.6  when x is 21.

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3. Suppose y varies directly with x, and y = 15 y equals 15  when x = 3 . x equals 3 .  What is y when x = 12 ? x equals 12 question mark