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Chapter 11: Q1. (page 673)

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

x
14812
y
281624

Short Answer

Expert verified

The table represents a direct 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�2=24鈰�8=328鈰�16=12812鈰�24=288

The product is not constant so the table doesn鈥檛 represent an inverse variation.

03

Step 3. Check for direct variation.

Find yxeach ordered pair from the table and get,

21=284=2168=22412=2

Since, the yx=2, for all given values of xand y, so the table represents the direct variation of y=2x.

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