In each example, find the constant of proportionality and write the equation of variation.

(1) The quantity y varies directly as x. When the value of y is 20, the value of x is 4.

(2) p α q. When p is 12, the value of q is 18.

(3) c α d. When c = 28, d = 21.

(4) m α n. When m = 7.5, n = 10.

(1) given y ∝ x

Constant of proportionality =

When y is 20 x is 4 therefore

= = 5 …(i)

Therefore, constant of proportionality = 5

Equation of variation is given by taking the denominator ‘x’ in equation (i) from L.H.S to R.H.S i.e. y = 5x

(2) given p ∝ q

Constant of proportionality =

When p is 12 q is 18 therefore

= = …(i)

Therefore, constant of proportionality =

Equation of variation is given by taking the denominator ‘q’ in equation (i) from L.H.S to R.H.S

i.e. p = q

(3) given c ∝ d

Constant of proportionality =

When c is 28 d is 21 therefore

= = …(i)

Therefore, constant of proportionality =

Equation of variation is given by taking the denominator ‘d’ in equation (i) from L.H.S to R.H.S

i.e. c = d

(4) given m ∝ n

Constant of proportionality =

When m is 7.5 n is 10 therefore

= = 0.75 …(i)

Therefore, constant of proportionality = 0.75

Equation of variation is given by taking the denominator ‘n’ in equation (i) from L.H.S to R.H.S i.e. m = 0.75n