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On increasing a, b increases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other

Solution:

When a increases and b increases and a/b remains constant then we can write:

a ∝ b

a/b = k, where k = proportionality constant

Only when k is constant for various values of variables a and b, we can conclude that a and b are in direct proportion.

The table below reflects

a	1	2	3	4	5
b	3	6	9	12	15

a/b = 1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 1/3 = k

The constant k is 1/3 and a & b are said to vary directly with each other.

✦ Try This: On decreasing x, y decreases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other.

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

As we can see from the above table, as ‘x’ decreases, ‘y’ also decreases.

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

The constant k is 3 and hence x and y are said to be direct proportion

On decreasing x, y decreases in such a manner that a/b remains constant and positive, then a and b are said to vary directly with each other.

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

NCERT Exemplar Class 8 Maths Chapter 10 Problem 29

On increasing a, b increases in such a manner that a/b remains______ and positive, then a and b are said to vary directly with each other

Summary:

On increasing a, b increases in such a manner that a/b remains constant and positive, then a and b are said to vary directly with each other

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