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Direct Variation

Direct variation describes a relationship where two variables increase or decrease at the same rate, expressed as y varies directly as x. The general form can be represented as x ∝ xn or x = kxn, where k is a constant. An example illustrates how to express one variable in terms of another when they vary directly.

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27 views1 page

Direct Variation

Direct variation describes a relationship where two variables increase or decrease at the same rate, expressed as y varies directly as x. The general form can be represented as x ∝ xn or x = kxn, where k is a constant. An example illustrates how to express one variable in terms of another when they vary directly.

Uploaded by

vashnadevi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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2/4/25, 2:36 PM Direct Variation

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Direct Variation

1.1 Direct Variation

Definition of direct variation

Direct variation explains the relationship between two variables, such that when variable y increases, then variable x also increases at the
same rate and vice versa.

This relation can be written as y varies directly as x .

In general, for a direct variation, y varies directly as xn can be written as

x ∝ xn (variation relation) or x = kxn (equation relation)


​ ​

1 1
where n = 1, 2, 3, , and k is a constant.
2 3
​ ​

Example 1

Given m = 12 when n = 3.

Express m in terms of n if

a) m varies directly as n.
b) m varies directly as n3 .

Solution:

a) n ⟹ m = kn … (1).

Substitute m = 12 and n = 3 into (1)


12
12 = k(3) ⟹ k = = 4.
3
​

∴ m = 4n.

b) m ∝ n3 ⟹ m = ln3 … (2).

Substitute m = 12 and n = 3 into (2):


12 4
12 = l(3)3 ⟹ l = =
27 9
​ ​

4 3
∴m= n .
9

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