5.1 Direct Variation (Part 3)

(D) Solving problems involving direct variations

1. If

y \propto x^{n}, where n = \frac{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 \propto x^{n}

and sufficient information is given, the values of variable x or variable y can be determined.

Example

y varies directly to x³and 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 y 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

y = 2(4)³ = 128

where k is a constant.