Question

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Answer 1

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

What is the directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

$m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}$

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

$m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}$

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

Learn more about Directly and Inversely proportional relationships:

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