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Algebra (Higher) - Algebraic Direct and Inverse Proportion
 
Direct Proportion (Algebraic) | Inverse Proportion
 
Direct Proportion (Algebraic)

If two variables y and x are in direct proportion we can write down an equation connecting them.

Equation for direct proportion
  y = kx  where k is a constant.

  
Examples of problems

1) Given that y is directly proportional to x and that y = 56 when x = 8. Calculate y when x = 12.
 
a) find the value of k y = kx x = 8 y = 56

56 = k x 8
 

k = 56/8
 

k = 7
 
 
 		  
b) substitute k = 7 into the equation

 

 y = 7x

 

 "when x = 12"
      
 y = 7 x 12
 
y = 84


2) Given that p is directly proportional to t2 and that p = 16 when t = 2.
 

a) Calculate p when t = 5

b) Calculate t when p = 81
 

a) p = kt2  
     
  16 = k x 4
 		  
  k = 4
 		  
p = 4t2
  		(t = 5)
 
  p = 4 x 25
 		  
p = 100
   
b) p = 4t2 		 
(p = 81)
                  81 = 4 x t2
  		 
                  t2 = 81/4
 		  
                  t = 9/2

                t = 4.5		  

Inverse Proportion

If two variables y and x are in inverse proportion, the equation is y = k/x

Examples of problems
1) If y is inversely proportion to x and y = 5 when x = 4,
  a) Calculate y when x = 10
 		 b) Calculate x when y = 40
 
a) y = k/x
 
  5 = k/4
   
  k = 20
     
  y = 20/x
 		 x = 10
 
  y=20/10
 
  y=2
   
  b) 40 = 20/x
  x = 0.5
   
If f is inversely proportional square_root_symbol w and f = 10 when w = 16.
a) calculate f when w = 9 b) calculate w when f = 4
  a) f = k/square_root_symbolw  
     
  10 = k/square_root_symbol16  
     
  10 = k/4
 
k = 40		  
     
  f = 40/square_root_symbol9
 		 w = 9
 
  f = 40/3
 
f = 13.3 (1dp)		  
     
  b) 4 = 40/square_root_symbol w  
     
  vw = 40/4  
     
  square_root_symbolw =10
 
w = 100