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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.
<h3>What is the directly proportional and inversely proportional relationship?</h3>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
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
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
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