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Question

Find constant of variation and write equation of variation for every example given below.
(1) p ∝ 1q ; if p = 15 then q = 4
(2) z ∝ 1w ; when z = 2.5 then w = 24
(3) s ∝ 1t2 ; if s = 4 then t = 5
(4) x ∝ 1y ; if x = 15 then y = 9

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Solution


(1)
p1q

p=kq, where k is constant of variation

When p = 15, q = 4.

15=k4k=15×4=60
So, the equation of variation is p=60q or pq = 60.

(2)
z1w

z=kw, where k is constant of variation

When z = 2.5, w = 24.

2.5=k24k=2.5×24=60
So, the equation of variation is z=60w or zw = 60.

(3)
s1t2

s=kt2, where k is constant of variation

When s = 4, t = 5.

4=k52 4=k25k=25×4=100
So, the equation of variation is s=100t2 or st2 = 100.

(4)
x1y

x=ky, where k is constant of variation

When x = 15, y = 9.

15=k915=k3k=15×3=45
So, the equation of variation is x=45y or xy=45.

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