Question

Determine if the relationship between the variables represents direct, inverse variation, or neither.

(-2, 10) (1, -5) (3, -15) (6, -30)

The volume, V of gas varies inversely with the Pressure, P on it. If the volume is 320 cm3 under pressure of 40 kg/cm2, what pressure has to be applied to have a volume of 200 cm3?

Answer 1

Represent the data in table form.

  x    y
---  -----
 -2   10
  1   -5
  3  -15
  6  -30

Let y = k*x  where k = constant.
Test x = -2:
 k*(-2) = 10
k = -5

Test x = 1:
k*x = -5*1 = -5  Correct

Test x = 3:
k*x = -5*3 = -15 Correct

Test x = 6:
k*x = -5*6 = -30  Correct

Therefore the relation is
y = -5x,  which is a direct variation.

Answer:  direct variation.

Because the volume, V varies inversely as pressure, P, let
 V = c/P  where c =  constant

Set V = 320 cm³,  P = 40 kg/cm².
320 = c/40
c = 320*40 = 12800
Therefore
V = 12800/P

When V = 200 cm³, obtain
  200 = 12800/P
200P = 12800 
       P = 12800/200 = 64 kg/cm²

Answer:  P = 64 kg/cm²