5.1 Direct Variation Part 2

(D) Solving problems involving direct variations
1. If   y x n , where n = 1 2 , 2 , 3 ,  then the equation is y = k x n where k is a constant.
2. The graph of y against xn is a straight line passing through the origin.
3.  If   y x n and sufficient information is given, the values of variable x or variable y can be determined.

Example
y varies directly to x3 and if y = 54 when x = 3, find
(a) The value of when y = 16
(b) The value of y when x = 4

Solution:
Given α x3, y = kx3
When y = 54, x = 3,
54 = k(3)3
54 = 27k
k = 2
Therefore y = 2x3

(a) When y = 16
 16 = 2x³
  x³ = 8
   x = 2

(b)
When x = 4
= 2(4)³ = 128
where k is a constant.

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