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x and y are said to vary directly with each other if for some positive number k, ______ = k

Solution:

Consider the following table showing the direct relationship between two variables x and y.

x	1	2	3	4	5
y	3	6	9	12	15

Let us investigate the relationship x/y by using all the table values of x and y

x/y = 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 1/3 = k

Since k is a constant we can state that there exists a relationship between variable x and y which is of direct proportion. In other words x and y vary directly

Hence we see that the relationship between x and y is of direct variation.As x increases, y also increases.

x and y are said to vary directly with each other if for some positive number k, x/y = k

Try This: Identify the relationship between the variables x and y from the values given in the table below:

x	1/6	1/12	1/18	1/14	1/16
y	1/3	1/6	1/9	1/7	1/8

Let us assume that xy = k

xy = 1/6 × 1/3 ≠1/12 × 1/6 ≠ 1/18 × 1/9 ≠ 1/14 × 1/7 ≠ 1/16 ×1/8 ≠ k

Hence the relationship between the variables is not inverse in nature

Let us assume x/y = k

x/y = 1/6/(1/3) = 1/12/(1/6) = 1/18/(1/9) = 1/14/(1/7) = 1/16/(1/8)=1/2 = k

Hence the variables are varying directly with each other.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 22

x and y are said to vary directly with each other if for some positive number k, x/y= k

Summary:

x and y are said to vary directly with each other if for some positive number k, xy =k

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