Question

If A varies directly as b and A=6, when b=1/3, find the equation that relates A and b.

Answer 1

a = 18b

Explanation:

Given that a varies directly as b then the equation relating them is

a = kb ← k is the constant of variation

To find k use the condition that a = 6 when b =
`(1)/(3)` , thus

k =
`(a)/(b)` =
`(6)/((1)/(3) )` = 18

a = 18b ← equation of variation

Answer 2

A = 18b

Explanation:

A = kb

6 = k(⅓)

k = 6×3

k = 18

A = 18b