5.1 Direct Variation Part 2

(D) Solving problems involving direct variations

1. If   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  $y\propto {x}^{n}$ 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 x 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