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Chapter 2: Q22. (page 107)

Compare the quantity in Column A and the quantity in Column B. Then determine whether:

A. the quantity in Column A is greater,

B. the quantity in Column B is greater,

C. the two quantities are equal, or

D. the relationship cannot be determined from the information given.

Column A

Column B

The slope of linem

1

Short Answer

Expert verified

Thequantity in Column A is greater. Option A is correct.

Step by step solution

01

Step-1 – Apply the concept of slope

The slope of the line passing through the points x1,y1andx2,y2 is expressed below.

m=y2-y1x2-x1

02

Step-2 –Substitute and solve

Consider the figure provided below.



Consider the ordered pairs 1-k,0and0,k.

Here x1,y1=1-k,0andx2,y2=0,k.

Recall the formula of slope of the line and apply it.

m=y2鈭�y1x2鈭�x1=k鈭�00鈭�1鈭�k=kk鈭�1
03

Step-3 – Compare the columns A and B

The value in column B is 1. The value obtained in column A is kk-1. Now, the value kk-1 is always greater than 1 because numerator k is greater than denominator k-1.

Hence, the quantity in Column A is greater.

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