Question

Relationship a is defined by the equation y=9x some values of relationship b are (0,0)(3,34.5)(5,57.5)(8,92) both relationships have a direct proportion between x and y. The rate of change of relationship b is how many units greater then the rate of change of relationship a

Answer 1

The rate of change of relationship 'b' is 2.5 times greater than the rate of change of relationship 'a'

Explanation:

The given parameters are;

The function representing relationship 'a' is y = 9·x

Some values of relationship 'b' are;

(0, 0), (3, 34.5), (5, 57.5), and (8, 92)

For direct proportionality of relationship 'b' we have;

y = k₂·x

∴ k₂ = y/x

∴ k₂ = 34.5/3 = 23/2

57.5/5 = 23/2

92/8 = 23/2

k₂ = 23/2

Therefore, the direct proportionality relationship of relationship 'a' is y = 9·x

∴ k₁ = 9

Therefore, the rate of change of relationship 'b' is k₂ - k₁ = (23/2) - 9 = 2.5 times greater than the rate of change of relationship 'a'.