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Chapter 11: Q2. (page 673)

Determine whether each table or equation represents an inverse or a direct variation. Explain.

x
1234
y
241286

Short Answer

Expert verified

The table represents an inverse variation.

Step by step solution

01

Step 1. State the concept of direct variation and inverse variation.

The relationship of the form y=kxis called direct variation.

Relationship of the form xy=kor y=kxwhere x,y鈮�0for some nonzero constant kis known as inverse variation i.e., yvaries inversely as x.

02

Step 2. Check for inverse variation. 

Find xyeach ordered pair from the table and get,

1鈰�24=242鈰�12=243鈰�8=244鈰�6=24

The product is constant so the table represents an inverse variation.

03

Step 3. Check for direct variation.

Find yxeach ordered pair from the table and get,

241=24122=683=2.6764=1.5

Since yxis not constant for any given values of xand y, so the table doesn鈥檛 represent the direct variation.

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