Answer:
The relationship between a and b ⇒ b = 10a
Step-by-step explanation:
The variable y is related to x by y= ax- b
When x has median 20
∴ y = 20a - b ⇒ (1)
interquartile range of y is the difference between two values of y
IQR of y = (ax₂ - b) - (ax₁- b)
= ax₂ - b - ax₁ + b
= ax₂ - ax₁
= a ( x₂ - x₁)
Where (x₂ - x₁) = interquartile range of x
∴ IQR of y = ax
When interquartile range of x = 10
y = 10a ⇒ (2)
median of y equals the interquartile range of y
From (1) and (2)
∴ 20a - b = 10a
Combine like terms
∴ 20a - 10a = b
∴ b = 10a
So, The relationship between a and b ⇒ b = 10a
