It is given that y is directly proportional to x. When x = 3, y = 18. (a) Find the equation connecting x and y. (b) Hence, find (i) the value of y when x = : 12, (ii) the value of x when y = 42.

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Step-by-step explanation:

(a)

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition when x = 3, y = 18 , then

18 = 3k ( divide both sides by 3 )

6 = k

y = 6x ← equation of proportion

(b)

(i)

when x = 12 , then

y = 6 × 12 = 72

(ii)

when y = 42

42 = 6x ( divide both sides by 6 )

7 = x

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